%PDF-1.6
%
1 0 obj
<>
endobj
2 0 obj
<>stream
Yaron Orenstein, David Pellow, Guillaume Marçais, Ron Shamir, Carl Kingsford
Designing small universal k-mer hitting sets for improved analysis of high-throughput sequencing
www.ploscompbiol.org
www.ploscompbiol.org
endstream
endobj
3 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 17 0 R/Annots 18 0 R/Contents 19 0 R/TrimBox[0 0 612 792]>>
endobj
18 0 obj
[20 0 R 21 0 R 22 0 R 23 0 R 24 0 R 25 0 R 26 0 R]
endobj
20 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref001)>>
endobj
21 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref002)>>
endobj
22 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref003)>>
endobj
23 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref004)>>
endobj
24 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref005)>>
endobj
25 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref006)>>
endobj
26 0 obj
<>/Border[0 0 0]/A 27 0 R>>
endobj
27 0 obj
<>
endobj
19 0 obj
[28 0 R 29 0 R 30 0 R 31 0 R 32 0 R 33 0 R 34 0 R 35 0 R]
endobj
28 0 obj
<>stream
q
0.955 g
0 w
199.9998 713.9999 m
575.9997 713.9999 l
575.9997 637.0002 l
199.9998 637.0002 l
f*
0.83 0.64 0.02 0 k
328.3087 450.9354 m
333.0709 450.9354 l
h
f*
337.4929 450.9354 m
342.2551 450.9354 l
h
f*
338.2866 178.9228 m
343.0488 178.9228 l
h
f*
263.1685 113.8961 m
267.9307 113.8961 l
h
f*
502.3559 81.9213 m
507.1181 81.9213 l
h
f*
511.5402 81.9213 m
516.3024 81.9213 l
h
f*
0 g
1 j
1 J
10 0 0 10 209.9905 696.9826 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(In)Tj
1.1111 0 Td
(this)Tj
1.6725 0 Td
(work,)Tj
2.5058 0 Td
(we)Tj
1.3266 0 Td
(create)Tj
2.5965 0 Td
(universal)Tj
/F10 1 Tf
3.8494 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6532 0 Td
(hitting)Tj
2.8913 0 Td
(sets)Tj
1.6611 0 Td
(that)Tj
1.7802 0 Td
(hit)Tj
1.3153 0 Td
(any)Tj
/F10 1 Tf
1.6554 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.8686 0 Td
(sequence.)Tj
4.0819 0 Td
(We)Tj
1.6101 0 Td
(pres-)Tj
-33.579 -1.2982 Td
(ent)Tj
1.491 0 Td
(several)Tj
2.9366 0 Td
(heuristic)Tj
3.6851 0 Td
(approaches)Tj
4.7338 0 Td
(for)Tj
1.389 0 Td
(constructing)Tj
5.261 0 Td
(such)Tj
2.058 0 Td
(small)Tj
2.33 0 Td
(sets;)Tj
1.8879 0 Td
(the)Tj
1.4683 0 Td
(approaches)Tj
4.7395 0 Td
(vary)Tj
1.9332 0 Td
(in)Tj
-33.9134 -1.2983 Td
(the)Tj
1.4683 0 Td
(trade-off)Tj
3.7077 0 Td
(between)Tj
3.5319 0 Td
(the)Tj
1.4684 0 Td
(size)Tj
1.6837 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4684 0 Td
(produced)Tj
4.0478 0 Td
(set)Tj
1.3039 0 Td
(and)Tj
1.7292 0 Td
(runtime)Tj
3.4752 0 Td
(and)Tj
1.7348 0 Td
(memory)Tj
3.6113 0 Td
(usage.)Tj
2.6589 0 Td
(We)Tj
-32.9043 -1.3039 Td
(show)Tj
2.3017 0 Td
(the)Tj
1.4683 0 Td
(benefit)Tj
2.9764 0 Td
(in)Tj
1.0374 0 Td
(practice)Tj
3.3789 0 Td
(of)Tj
1.0148 0 Td
(using)Tj
2.3868 0 Td
(the)Tj
1.4683 0 Td
(produced)Tj
4.0479 0 Td
(universal)Tj
/F10 1 Tf
3.855 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6476 0 Td
(hitting)Tj
2.8913 0 Td
(sets)Tj
1.6668 0 Td
(compared)Tj
-31.1412 -1.2983 Td
(to)Tj
1.0261 0 Td
(minimizers)Tj
4.7792 0 Td
(and)Tj
1.7291 0 Td
(randomly)Tj
4.1272 0 Td
(created)Tj
3.1238 0 Td
(hitting)Tj
2.8913 0 Td
(sets)Tj
1.6668 0 Td
(on)Tj
1.2755 0 Td
(the)Tj
1.4684 0 Td
(human)Tj
3.0784 0 Td
(genome.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 599.0173 cm
BT
/F3 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(Introduction)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 582.0094 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(The)Tj
1.7801 0 Td
(pace)Tj
2.0183 0 Td
(of)Tj
1.0147 0 Td
(high-throughput)Tj
6.9279 0 Td
(sequencing)Tj
4.7168 0 Td
(keeps)Tj
2.4378 0 Td
(accelerating)Tj
4.9833 0 Td
(as)Tj
1.0148 0 Td
(it)Tj
0.7823 0 Td
(becomes)Tj
3.685 0 Td
(cheaper)Tj
3.3392 0 Td
(and)Tj
1.7348 0 Td
(faster)Tj
-34.435 -1.2982 Td
(and)Tj
1.7291 0 Td
(with)Tj
1.9956 0 Td
(it)Tj
0.788 0 Td
(the)Tj
1.4683 0 Td
(need)Tj
2.143 0 Td
(for)Tj
1.389 0 Td
(faster)Tj
2.3924 0 Td
(and)Tj
1.7291 0 Td
(more)Tj
2.3414 0 Td
(memory)Tj
3.617 0 Td
(efficient)Tj
3.4469 0 Td
(genomic)Tj
3.6794 0 Td
(analysis)Tj
3.3221 0 Td
(methods)Tj
3.6851 0 Td
(grows.)Tj
-33.7264 -1.3039 Td
(The)Tj
1.7801 0 Td
(NIH)Tj
2.0636 0 Td
(Sequence)Tj
3.9742 0 Td
(Read)Tj
2.228 0 Td
(Archive,)Tj
3.5943 0 Td
(for)Tj
1.3889 0 Td
(example,)Tj
3.7758 0 Td
(currently)Tj
3.8834 0 Td
(contains)Tj
3.6057 0 Td
(over)Tj
1.9785 0 Td
(12)Tj
1.1736 0 Td
(petabases)Tj
3.9798 0 Td
(of)Tj
-33.4259 -1.2983 Td
(sequence)Tj
3.855 0 Td
(data)Tj
1.9163 0 Td
(and)Tj
1.7291 0 Td
(is)Tj
0.8504 0 Td
(growing)Tj
3.5262 0 Td
(at)Tj
0.9525 0 Td
(a)Tj
0.6519 0 Td
(fast)Tj
1.6044 0 Td
(pace.)Tj
2.2451 0 Td
(Increased)Tj
4.0705 0 Td
(use)Tj
1.5307 0 Td
(of)Tj
1.0148 0 Td
(sequence-based)Tj
6.4629 0 Td
(assays)Tj
2.6249 0 Td
(\(DNA)Tj
-33.0347 -1.2983 Td
(sequencing,)Tj
4.9379 0 Td
(RNA-seq,)Tj
4.1329 0 Td
(numerous)Tj
4.3029 0 Td
(other)Tj
2.3471 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 361.1905 533.6503 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 365.159 530.022 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(-seqs\))Tj
2.9536 0 Td
(in)Tj
1.0375 0 Td
(research)Tj
3.5546 0 Td
(and)Tj
1.7348 0 Td
(in)Tj
1.0318 0 Td
(clinical)Tj
3.0784 0 Td
(settings)Tj
3.2428 0 Td
(creates)Tj
-33.148 -1.3039 Td
(high)Tj
2.0013 0 Td
(computational)Tj
6.0434 0 Td
(processing)Tj
4.456 0 Td
(burdens.)Tj
3.7077 0 Td
(Metagenomic)Tj
5.7202 0 Td
(studies)Tj
2.9763 0 Td
(generate)Tj
3.6057 0 Td
(even)Tj
2.0636 0 Td
(larger)Tj
2.5228 0 Td
(sequencing)Tj
-33.097 -1.2982 Td
(datasets.)Tj
3.583 0 Td
(New)Tj
2.0636 0 Td
(fundamental)Tj
5.3177 0 Td
(computational)Tj
6.0434 0 Td
(ideas)Tj
2.2337 0 Td
(are)Tj
1.4513 0 Td
(essential)Tj
3.583 0 Td
(to)Tj
1.0261 0 Td
(manage)Tj
3.3449 0 Td
(and)Tj
1.7291 0 Td
(analyze)Tj
3.1748 0 Td
(these)Tj
-33.5506 -1.2983 Td
(data.)Tj
1.1962 -1.3039 Td
(The)Tj
1.7858 0 Td
(minimizer)Tj
4.4164 0 Td
(approach)Tj
3.9515 0 Td
(has)Tj
1.542 0 Td
(been)Tj
2.126 0 Td
(extremely)Tj
4.1441 0 Td
(successful)Tj
4.1612 0 Td
(in)Tj
1.0375 0 Td
(increasing)Tj
4.3313 0 Td
(the)Tj
1.4683 0 Td
(efficiency)Tj
4.0252 0 Td
(of)Tj
1.0148 0 Td
(sev-)Tj
-35.2003 -1.2983 Td
(eral)Tj
1.6951 0 Td
(sequence)Tj
3.8551 0 Td
(analysis)Tj
3.3279 0 Td
(challenges.)Tj
4.5467 0 Td
(Given)Tj
2.6249 0 Td
(a)Tj
0.6575 0 Td
(sequence)Tj
3.8551 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7326 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9751 0 Td
(its)Tj
/F10 1 Tf
1.1452 0 Td
[()18()12()18()12()18()-3()2()]TJ
/F9 1 Tf
4.2689 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4684 0 Td
(lexico-)Tj
-33.0177 -1.2982 Td
(graphically)Tj
4.6034 0 Td
(smallest)Tj
/F10 1 Tf
3.4129 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6476 0 Td
(in)Tj
1.0375 0 Td
(it)Tj
0.788 0 Td
([)Tj
0.83 0.64 0.02 0 k
(1)Tj
0 g
(,)Tj
0.83 0.64 0.02 0 k
1.2586 0 Td
(2)Tj
0 g
(].)Tj
1.2642 0 Td
(For)Tj
1.6213 0 Td
(a)Tj
0.6576 0 Td
(sequence)Tj
/F10 1 Tf
3.8551 0 Td
[( )]TJ
/F9 1 Tf
0.6747 0 Td
(of)Tj
1.0148 0 Td
(any)Tj
1.6611 0 Td
(length)Tj
2.7269 0 Td
(its)Tj
/F10 1 Tf
1.1452 0 Td
[()18()12()18()12()18()-3()2()]TJ
4.2746 0 Td
[(\n)-3()8()]TJ
/F9 1 Tf
1.2359 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4683 0 Td
(set)Tj
-36.1981 -1.304 Td
(of)Tj
1.0148 0 Td
(minimizers)Tj
4.7792 0 Td
(of)Tj
1.0148 0 Td
(every)Tj
/F10 1 Tf
2.3471 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.8629 0 Td
(subsequence)Tj
5.2553 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[( )]TJ
/F9 1 Tf
(.)Tj
0.8957 0 Td
(Hence,)Tj
3.0331 0 Td
(every)Tj
2.3471 0 Td
(window)Tj
3.4412 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7269 0 Td
[()]TJ
/F9 1 Tf
0.7484 0 Td
(in)Tj
/F10 1 Tf
1.0374 0 Td
[( )]TJ
/F9 1 Tf
0.6747 0 Td
(is)Tj
0.8447 0 Td
(repre-)Tj
-35.0756 -1.2982 Td
(sented)Tj
2.8006 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(set,)Tj
1.5307 0 Td
(and)Tj
1.7292 0 Td
(a)Tj
0.6519 0 Td
(minimizer)Tj
4.4164 0 Td
(set)Tj
1.3039 0 Td
(for)Tj
1.389 0 Td
(a)Tj
0.6518 0 Td
(sequence)Tj
/F10 1 Tf
3.8551 0 Td
[( )]TJ
/F9 1 Tf
0.6803 0 Td
(constitutes)Tj
4.5298 0 Td
(a)Tj
0.6576 0 Td
(succinct)Tj
3.4923 0 Td
(representation)Tj
6.015 0 Td
(for)Tj
-36.2094 -1.2983 Td
(it.)Tj
1.0091 0 Td
(As)Tj
1.2643 0 Td
(we)Tj
1.3266 0 Td
(discuss)Tj
3.05 0 Td
(below,)Tj
2.812 0 Td
(minimizers)Tj
4.7792 0 Td
(have)Tj
2.0636 0 Td
(had)Tj
1.7063 0 Td
(numerous)Tj
4.3087 0 Td
(applications)Tj
5.0399 0 Td
(in)Tj
1.0375 0 Td
(sequence)Tj
3.8551 0 Td
(analysis.)Tj
-31.0561 -1.2983 Td
(Here,)Tj
2.4321 0 Td
(we)Tj
1.321 0 Td
(generalize)Tj
4.2349 0 Td
(and)Tj
1.7291 0 Td
(improve)Tj
3.5773 0 Td
(on)Tj
1.2699 0 Td
(the)Tj
1.4683 0 Td
(minimizer)Tj
4.4107 0 Td
(idea.)Tj
2.0976 0 Td
(To)Tj
1.3323 0 Td
(avoid)Tj
2.4094 0 Td
(dependence)Tj
5.0003 0 Td
(on)Tj
1.2756 0 Td
(a)Tj
0.6519 0 Td
(particu-)Tj
-34.4066 -1.3039 Td
(lar)Tj
1.2699 0 Td
(sequence)Tj
/F10 1 Tf
3.8608 0 Td
[( )]TJ
/F9 1 Tf
(,)Tj
0.8957 0 Td
(we)Tj
1.3323 0 Td
(introduce)Tj
4.1102 0 Td
(the)Tj
1.474 0 Td
(notion)Tj
2.8913 0 Td
(of)Tj
1.0204 0 Td
(a)Tj
0.652 0 Td
(universal)Tj
3.8551 0 Td
(hitting)Tj
2.8913 0 Td
(set.)Tj
1.525 0 Td
(For)Tj
1.6271 0 Td
(integers)Tj
/F10 1 Tf
3.3789 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
0.9127 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9695 0 Td
(a)Tj
0.6576 0 Td
(set)Tj
/F10 1 Tf
1.3039 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 553.2094 385.3417 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 564.548 386.9858 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
-36.4533 -1.2982 Td
(called)Tj
2.5172 0 Td
(a)Tj
/F10 1 Tf
0.6576 0 Td
[(\r)12()18()15()3()2()5(\n)-3()11()]TJ
3.7814 0 Td
[()18()14()7()12()13()]TJ
2.795 0 Td
[(\n)-3()8()]TJ
/F9 1 Tf
1.2415 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(\(UHS\))Tj
2.88 0 Td
(if)Tj
0.7767 0 Td
(every)Tj
2.347 0 Td
(possible)Tj
3.4129 0 Td
(sequence)Tj
3.8551 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7326 0 Td
[()]TJ
/F9 1 Tf
0.7427 0 Td
(must)Tj
2.228 0 Td
(con-)Tj
-35.0077 -1.2983 Td
(tain)Tj
1.7688 0 Td
(at)Tj
0.9525 0 Td
(least)Tj
1.9785 0 Td
(one)Tj
/F10 1 Tf
1.7008 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6532 0 Td
(from)Tj
/F10 1 Tf
2.2054 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 319.5212 359.3196 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 328.6488 361.0204 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
0.4422 0 Td
(The)Tj
1.7858 0 Td
(set)Tj
1.3039 0 Td
(of)Tj
1.0148 0 Td
(all)Tj
/F10 1 Tf
1.1452 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(is)Tj
0.8447 0 Td
(a)Tj
0.6576 0 Td
(trivial)Tj
2.5568 0 Td
(UHS,)Tj
2.4265 0 Td
(but)Tj
1.5534 0 Td
(it)Tj
0.7823 0 Td
(does)Tj
2.041 0 Td
(not)Tj
1.576 0 Td
(provide)Tj
-34.0041 -1.3039 Td
(any)Tj
1.6554 0 Td
(useful)Tj
2.5966 0 Td
(reduction)Tj
4.1102 0 Td
(in)Tj
1.0374 0 Td
(computational)Tj
6.049 0 Td
(resources)Tj
3.9912 0 Td
(needed.)Tj
3.3165 0 Td
(Hence,)Tj
3.0331 0 Td
(our)Tj
1.627 0 Td
(main)Tj
2.2904 0 Td
(computational)Tj
-29.7068 -1.2982 Td
(problem)Tj
3.6113 0 Td
(is:)Tj
/F10 1 Tf
-2.4151 -1.2983 Td
[()2()20()13()10()4()2()]TJ
3.4809 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.9071 0 Td
(Given)Tj
/F10 1 Tf
2.6306 0 Td
[()]TJ
/F9 1 Tf
0.6859 0 Td
(and)Tj
/F10 1 Tf
1.7292 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9751 0 Td
(find)Tj
1.8481 0 Td
(a)Tj
0.6576 0 Td
(smallest)Tj
3.4072 0 Td
(universal)Tj
3.8551 0 Td
(hitting)Tj
2.8913 0 Td
(set)Tj
1.304 0 Td
(of)Tj
/F10 1 Tf
1.0147 0 Td
[()]TJ
/F9 1 Tf
(-mers.)Tj
-25.3868 -1.3039 Td
(A)Tj
0.9071 0 Td
(small)Tj
2.3244 0 Td
(UHS)Tj
2.1997 0 Td
(has)Tj
1.542 0 Td
(a)Tj
0.6576 0 Td
(variety)Tj
2.9254 0 Td
(of)Tj
1.0148 0 Td
(applications)Tj
5.0398 0 Td
(in)Tj
1.0318 0 Td
(speeding)Tj
3.7588 0 Td
(up)Tj
1.2642 0 Td
(genomic)Tj
3.6737 0 Td
(analyses)Tj
3.4809 0 Td
(since)Tj
2.245 0 Td
(it)Tj
0.7824 0 Td
(can)Tj
1.6271 0 Td
(be)Tj
-35.6709 -1.2983 Td
(used)Tj
2.0579 0 Td
(where)Tj
2.6533 0 Td
(minimizers)Tj
4.7735 0 Td
(have)Tj
2.0636 0 Td
(been)Tj
2.1202 0 Td
(used)Tj
2.0579 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(past.)Tj
2.058 0 Td
(For)Tj
1.6271 0 Td
(example:)Tj
-21.9173 -1.8992 Td
(1.)Tj
/F16 1 Tf
1.2019 0 Td
(Hashing)Tj
3.7247 0 Td
(for)Tj
1.4683 0 Td
(read)Tj
2.0693 0 Td
(overlapping.)Tj
/F9 1 Tf
5.4594 0 Td
(A)Tj
0.9071 0 Td
(na)Tj
/F17 1 Tf
[()]TJ
/F9 1 Tf
(ve)Tj
2.3357 0 Td
(read)Tj
1.9786 0 Td
(overlapper)Tj
4.4844 0 Td
(must)Tj
2.228 0 Td
(test)Tj
/F10 1 Tf
1.5987 0 Td
[()]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 490.2236 281.4236 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 493.7385 277.0015 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\))Tj
0.5612 0 Td
(pairs)Tj
2.1713 0 Td
(of)Tj
1.0148 0 Td
(reads)Tj
2.3358 0 Td
(to)Tj
-34.2536 -1.2982 Td
(see)Tj
1.423 0 Td
(whether)Tj
3.4809 0 Td
(they)Tj
1.9219 0 Td
(overlap)Tj
3.1748 0 Td
(\(where)Tj
/F10 1 Tf
2.9877 0 Td
[()]TJ
/F9 1 Tf
0.7483 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(reads\).)Tj
2.9027 0 Td
(If)Tj
0.8504 0 Td
(we)Tj
1.3266 0 Td
(require)Tj
3.1123 0 Td
(an)Tj
1.2019 0 Td
(overlap)Tj
3.1747 0 Td
(of)Tj
-33.0573 -1.3039 Td
(length)Tj
/F10 1 Tf
2.7269 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9751 0 Td
(any)Tj
1.6555 0 Td
(pair)Tj
1.8085 0 Td
(of)Tj
1.0148 0 Td
(reads)Tj
2.3414 0 Td
(with)Tj
1.9955 0 Td
(such)Tj
2.058 0 Td
(an)Tj
1.2019 0 Td
(overlap)Tj
3.1747 0 Td
(must)Tj
2.2281 0 Td
(share)Tj
2.3357 0 Td
(a)Tj
/F10 1 Tf
0.6576 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6476 0 Td
(from)Tj
2.2052 0 Td
(set)Tj
/F10 1 Tf
1.3039 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 522.3118 249.3354 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 533.5937 250.9795 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(in)Tj
1.0374 0 Td
(this)Tj
-33.1934 -1.2982 Td
(overlapped)Tj
4.6318 0 Td
(region.)Tj
3.0217 0 Td
(By)Tj
1.2473 0 Td
(bucketing)Tj
4.1725 0 Td
(reads)Tj
2.3301 0 Td
(into)Tj
1.8312 0 Td
(bins)Tj
1.8992 0 Td
(according)Tj
4.1782 0 Td
(to)Tj
1.0205 0 Td
(the)Tj
1.4626 0 Td
(universal)Tj
/F10 1 Tf
3.8495 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
2.9989 0 Td
(they)Tj
1.9219 0 Td
(con-)Tj
-34.5654 -1.2983 Td
(tain,)Tj
1.9899 0 Td
(we)Tj
1.3266 0 Td
(need)Tj
2.143 0 Td
(only)Tj
1.9786 0 Td
(test)Tj
1.6044 0 Td
(pairs)Tj
2.1657 0 Td
(of)Tj
1.0147 0 Td
(reads)Tj
2.3414 0 Td
(in)Tj
1.0319 0 Td
(the)Tj
1.474 0 Td
(same)Tj
2.2563 0 Td
(bucket.)Tj
3.1238 0 Td
(The)Tj
1.7801 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
1.0148 0 Td
(buckets)Tj
3.2541 0 Td
(is)Tj
0.8503 0 Td
(limited)Tj
-32.7682 -1.3039 Td
(by)Tj
1.1792 0 Td
(|)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 233.348 210.3307 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 242.4188 211.9748 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(|.)Tj
-4.2406 -1.8992 Td
(2.)Tj
/F16 1 Tf
1.2019 0 Td
(Sparse)Tj
2.948 0 Td
(suffix)Tj
2.5738 0 Td
(arrays.)Tj
/F9 1 Tf
3.0444 0 Td
(A)Tj
0.9071 0 Td
(sparse)Tj
2.6872 0 Td
(suffix)Tj
2.4151 0 Td
(array)Tj
2.2847 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
0.6576 0 Td
(string)Tj
/F10 1 Tf
2.5285 0 Td
[( )]TJ
/F9 1 Tf
0.6747 0 Td
(saves)Tj
2.2563 0 Td
(memory)Tj
3.617 0 Td
(by)Tj
1.1792 0 Td
(storing)Tj
3.0387 0 Td
(an)Tj
1.2019 0 Td
(index)Tj
-33.029 -1.2982 Td
(for)Tj
1.3833 0 Td
(only)Tj
1.9785 0 Td
(every)Tj
/F10 1 Tf
2.3471 0 Td
[(\n)]TJ
/F9 1 Tf
(th)Tj
1.3776 0 Td
(position)Tj
3.4923 0 Td
(in)Tj
/F10 1 Tf
1.0318 0 Td
[( )]TJ
/F9 1 Tf
0.6746 0 Td
([)Tj
0.83 0.64 0.02 0 k
(3)Tj
0 g
(].)Tj
1.6044 0 Td
(To)Tj
1.3379 0 Td
(query)Tj
2.5059 0 Td
(a)Tj
0.6519 0 Td
(sparse)Tj
2.6873 0 Td
(suffix)Tj
2.4151 0 Td
(array)Tj
2.2903 0 Td
(for)Tj
1.3833 0 Td
(string)Tj
/F10 1 Tf
2.5342 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9184 0 Td
(we)Tj
1.3266 0 Td
(perform)Tj
3.5206 0 Td
(at)Tj
-35.4611 -1.2983 Td
(most)Tj
/F10 1 Tf
2.2054 0 Td
[(\n)]TJ
/F9 1 Tf
0.5499 0 Td
(queries)Tj
3.101 0 Td
(starting)Tj
3.2598 0 Td
(from)Tj
2.2053 0 Td
(indices)Tj
3.0388 0 Td
(0,)Tj
/F18 1 Tf
0 Tc
0.924 0 Td
(.)Tj
0.4309 0 Td
(.)Tj
0.4365 0 Td
(.)Tj
/F9 1 Tf
-0.004 Tc
(,)Tj
/F10 1 Tf
0.7144 0 Td
[(\n)]TJ
/F17 1 Tf
0.5499 0 Td
[()]TJ
/F9 1 Tf
0.788 0 Td
(1)Tj
0.6973 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[()]TJ
/F9 1 Tf
(;)Tj
0.9184 0 Td
(one)Tj
1.7008 0 Td
(of)Tj
1.0148 0 Td
(these)Tj
2.2564 0 Td
(queries)Tj
3.101 0 Td
(will)Tj
1.6611 0 Td
(intersect)Tj
3.634 0 Td
(a)Tj
-34.2252 -1.3039 Td
(position)Tj
3.4922 0 Td
(stored)Tj
2.7099 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.4683 0 Td
(suffix)Tj
2.4208 0 Td
(array.)Tj
2.5115 0 Td
(Using)Tj
/F10 1 Tf
2.5965 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 381.2598 152.3338 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 390.3874 153.9779 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4478 0 Td
(we)Tj
1.3266 0 Td
(can)Tj
1.6271 0 Td
(instead)Tj
3.0784 0 Td
(store)Tj
2.1827 0 Td
(only)Tj
1.9729 0 Td
(positions)Tj
3.8551 0 Td
(in)Tj
/F10 1 Tf
1.0374 0 Td
[( )]TJ
/F9 1 Tf
0.6747 0 Td
(that)Tj
-34.0381 -1.2982 Td
(start)Tj
1.9785 0 Td
(with)Tj
2.0013 0 Td
(a)Tj
/F10 1 Tf
0.652 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6532 0 Td
(in)Tj
/F10 1 Tf
1.0318 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 302.1732 139.3511 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 311.244 140.9952 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
0.4478 0 Td
(Any)Tj
1.9049 0 Td
(query)Tj
2.5058 0 Td
(with)Tj
1.9956 0 Td
(|)Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(|)Tj
/F15 1 Tf
0 Tc
1.2132 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F9 1 Tf
0.7427 0 Td
(must)Tj
2.228 0 Td
(contain)Tj
3.2485 0 Td
(one)Tj
1.7008 0 Td
(of)Tj
1.0148 0 Td
(these)Tj
2.2507 0 Td
(selected)Tj
/F10 1 Tf
3.3505 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
-33.5165 -1.2982 Td
(and)Tj
1.7291 0 Td
(will)Tj
1.6611 0 Td
(be)Tj
1.1508 0 Td
(matched)Tj
3.6737 0 Td
(when)Tj
2.4037 0 Td
(searching)Tj
4.0421 0 Td
(the)Tj
1.4741 0 Td
(suffix)Tj
2.4151 0 Td
(array.)Tj
2.5114 0 Td
(This)Tj
1.9843 0 Td
(approach)Tj
3.9514 0 Td
(has)Tj
1.5421 0 Td
(been)Tj
2.126 0 Td
(applied)Tj
3.1521 0 Td
(with)Tj
-33.817 -1.3039 Td
(minimizers)Tj
4.7735 0 Td
([)Tj
0.83 0.64 0.02 0 k
(4)Tj
0 g
(])Tj
1.3776 0 Td
(to)Tj
1.0261 0 Td
(good)Tj
2.228 0 Td
(effect.)Tj
-10.6071 -1.8992 Td
(3.)Tj
/F16 1 Tf
1.2019 0 Td
(Bloom)Tj
3.0047 0 Td
(filters)Tj
2.6702 0 Td
(to)Tj
1.0771 0 Td
(speed)Tj
2.5682 0 Td
(up)Tj
1.3152 0 Td
(sequence)Tj
3.9628 0 Td
(search.)Tj
/F9 1 Tf
3.1237 0 Td
(Bloom)Tj
2.88 0 Td
(filters)Tj
2.4775 0 Td
(have)Tj
2.0579 0 Td
(been)Tj
2.1203 0 Td
(used)Tj
2.0636 0 Td
(to)Tj
1.0205 0 Td
(speed)Tj
2.4775 0 Td
(up)Tj
-32.8192 -1.2983 Td
(sequence)Tj
3.855 0 Td
(search)Tj
2.761 0 Td
(by)Tj
1.1848 0 Td
(storing)Tj
/F10 1 Tf
3.0387 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0103 0 Td
(present)Tj
3.1635 0 Td
(in)Tj
1.0318 0 Td
(a)Tj
0.6576 0 Td
(read)Tj
1.9729 0 Td
(set)Tj
1.304 0 Td
(for)Tj
1.3889 0 Td
(quick)Tj
2.4378 0 Td
(testing)Tj
2.8857 0 Td
([)Tj
0.83 0.64 0.02 0 k
(5)Tj
0 g
(,)Tj
0.83 0.64 0.02 0 k
1.2585 0 Td
(6)Tj
0 g
(].)Tj
1.2643 0 Td
(In)Tj
1.1055 0 Td
(current)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 169.285 23.6976 re
W* n
q
169.2283 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 450.4818 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Compact)Tj
4.1669 0 Td
(universal)Tj
/F7 1 Tf
4.1386 0 Td
(k)Tj
/F0 1 Tf
(-mer)Tj
2.7355 0 Td
(hitting)Tj
2.8346 0 Td
(sets)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
142.5827 34.9228 m
295.8236 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(Computationa)Tj
6.1229 0 Td
(l)Tj
0.4322 0 Td
(Biology)Tj
3.4371 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https:/)Tj
2.6788 0 Td
(/doi.org/10.13)Tj
6.0094 0 Td
(71/journal.p)Tj
5.1166 0 Td
(cbi.1005777)Tj
0 g
6.3497 0 Td
(October)Tj
3.7276 0 Td
(2,)Tj
1.0346 0 Td
(2017)Tj
26.901 0 Td
(2)Tj
0.7654 0 Td
(/)Tj
0.496 0 Td
(15)Tj
/F12 1 Tf
-0.025 Tc
-66.402 84.0904 Td
(Absorptio)Tj
3.5929 0 Td
(n)Tj
0.6945 0 Td
(fellowship.)Tj
4.1811 0 Td
(This)Tj
1.7859 0 Td
(research)Tj
3.4157 0 Td
(is)Tj
0.8292 0 Td
(funded)Tj
2.7921 0 Td
(in)Tj
-17.2914 -1.3748 Td
(part)Tj
1.6795 0 Td
(by)Tj
1.1126 0 Td
(the)Tj
1.3677 0 Td
(Gordon)Tj
3.0119 0 Td
(and)Tj
1.5874 0 Td
(Betty)Tj
2.0976 0 Td
(Moore)Tj
2.6504 0 Td
(Foundation')Tj
4.3229 0 Td
(s)Tj
-17.83 -1.3749 Td
(Data-Driven)Tj
4.6205 0 Td
(Discove)Tj
2.9338 0 Td
(ry)Tj
0.9497 0 Td
(Initiative)Tj
3.3023 0 Td
(through)Tj
3.1536 0 Td
(Grant)Tj
-14.9599 -1.3748 Td
(GBMF455)Tj
3.7063 0 Td
(4)Tj
0.6945 0 Td
(to)Tj
0.9496 0 Td
(CK,)Tj
1.4953 0 Td
(by)Tj
1.1126 0 Td
(the)Tj
1.3748 0 Td
(US)Tj
1.3323 0 Td
(Nationa)Tj
2.8205 0 Td
(l)Tj
0.4181 0 Td
(Science)Tj
-13.904 -1.3748 Td
(Foundation)Tj
4.3512 0 Td
(\(CCF-125608)Tj
4.9252 0 Td
(7,)Tj
0.9213 0 Td
(CCF-131)Tj
3.1961 0 Td
(9998\))Tj
2.4236 0 Td
(and)Tj
1.5874 0 Td
(by)Tj
-17.4048 -1.3748 Td
(the)Tj
1.3677 0 Td
(US)Tj
1.3323 0 Td
(National)Tj
3.2386 0 Td
(Institutes)Tj
3.6496 0 Td
(of)Tj
0.9496 0 Td
(Health)Tj
-10.5378 -1.3748 Td
(\(R01HG00)Tj
3.9614 0 Td
(7104\).)Tj
2.6504 0 Td
(CK)Tj
1.2685 0 Td
(received)Tj
3.3024 0 Td
(support)Tj
3.0969 0 Td
(as)Tj
1.063 0 Td
(an)Tj
1.1126 0 Td
(Alfred)Tj
-16.4552 -1.3748 Td
(P.)Tj
0.9708 0 Td
(Sloan)Tj
2.3032 0 Td
(Research)Tj
3.6992 0 Td
(Fellow.)Tj
2.7851 0 Td
(The)Tj
1.5874 0 Td
(funders)Tj
3.0473 0 Td
(had)Tj
1.5874 0 Td
(no)Tj
1.1693 0 Td
(role)Tj
-17.1497 -1.3748 Td
(in)Tj
0.8858 0 Td
(study)Tj
2.2677 0 Td
(design,)Tj
2.8985 0 Td
(data)Tj
1.7929 0 Td
(collection)Tj
3.7347 0 Td
(and)Tj
1.5945 0 Td
(analysis)Tj
2.9622 0 Td
(,)Tj
-16.1363 -1.3748 Td
(decision)Tj
3.2882 0 Td
(to)Tj
0.9496 0 Td
(publish,)Tj
3.1465 0 Td
(or)Tj
0.9992 0 Td
(preparation)Tj
4.4433 0 Td
(of)Tj
0.9496 0 Td
(the)Tj
-13.7764 -1.3749 Td
(manuscript.)Tj
/F11 1 Tf
0 -2.126 Td
(Competing)Tj
4.3795 0 Td
(interests)Tj
3.3307 0 Td
(:)Tj
/F12 1 Tf
0.4819 0 Td
(The)Tj
1.5875 0 Td
(authors)Tj
3.0401 0 Td
(have)Tj
1.963 0 Td
(declared)Tj
-14.7827 -1.3748 Td
(that)Tj
1.6228 0 Td
(no)Tj
1.1693 0 Td
(competing)Tj
4.1599 0 Td
(interests)Tj
ET
endstream
endobj
29 0 obj
<>stream
endstream
endobj
30 0 obj
<>stream
endstream
endobj
31 0 obj
<>stream
endstream
endobj
32 0 obj
<>stream
endstream
endobj
33 0 obj
<>stream
endstream
endobj
34 0 obj
<>stream
endstream
endobj
35 0 obj
<>stream
BT
10.3394 66.8414 Td
(exist.)Tj
ET
Q
endstream
endobj
36 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 17 0 R/Annots 38 0 R/Contents 39 0 R/TrimBox[0 0 612 792]>>
endobj
38 0 obj
[40 0 R 41 0 R 42 0 R 43 0 R 44 0 R 45 0 R 46 0 R 47 0 R 48 0 R 49 0 R 50 0 R 51 0 R]
endobj
40 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref004)>>
endobj
41 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref007)>>
endobj
42 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref009)>>
endobj
43 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref001)>>
endobj
44 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref002)>>
endobj
45 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref010)>>
endobj
46 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref011)>>
endobj
47 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref012)>>
endobj
48 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref008)>>
endobj
49 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref013)>>
endobj
50 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref014)>>
endobj
51 0 obj
<>/Border[0 0 0]/A 52 0 R>>
endobj
52 0 obj
<>
endobj
39 0 obj
[53 0 R 54 0 R 55 0 R 56 0 R 57 0 R 58 0 R 59 0 R 60 0 R 61 0 R 62 0 R 63 0 R 64 0 R]
endobj
53 0 obj
<>stream
q
0.83 0.64 0.02 0 k
493.7953 648.3402 m
498.5575 648.3402 l
h
f*
502.9795 648.3402 m
507.7417 648.3402 l
h
f*
512.9008 648.3402 m
517.663 648.3402 l
h
f*
355.8047 635.3008 m
360.5669 635.3008 l
h
f*
433.5307 622.3181 m
438.2929 622.3181 l
h
f*
525.0331 622.3181 m
534.5575 622.3181 l
h
f*
353.1402 596.2961 m
362.6646 596.2961 l
h
f*
532.9134 583.3134 m
542.4378 583.3134 l
h
f*
255.515 557.348 m
260.2772 557.348 l
h
f*
337.9465 544.3087 m
347.4709 544.3087 l
h
f*
203.4142 518.3433 m
212.9386 518.3433 l
h
f*
0 g
1 j
1 J
0 w
10 0 0 10 212.0314 707.4141 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(implementations,)Tj
7.2226 0 Td
(all)Tj
/F10 1 Tf
1.1452 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0103 0 Td
(present)Tj
3.1635 0 Td
(in)Tj
1.0375 0 Td
(a)Tj
0.6519 0 Td
(read)Tj
1.9786 0 Td
(set)Tj
1.3039 0 Td
(are)Tj
1.4457 0 Td
(stored)Tj
2.7099 0 Td
(in)Tj
1.0375 0 Td
(these)Tj
2.2563 0 Td
(filters.)Tj
2.6986 0 Td
(If,)Tj
1.0715 0 Td
(instead,)Tj
3.3052 0 Td
(only)Tj
-34.0382 -1.3039 Td
(the)Tj
1.4683 0 Td
(set)Tj
1.3039 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(in)Tj
/F10 1 Tf
1.0318 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 297.2976 692.7307 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 308.5795 694.3748 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8503 0 Td
(stored,)Tj
2.9367 0 Td
(any)Tj
1.6554 0 Td
(window)Tj
3.4356 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F15 1 Tf
0 Tc
2.7326 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F9 1 Tf
0.7483 0 Td
(is)Tj
0.8448 0 Td
(still)Tj
1.6384 0 Td
(guaranteed)Tj
4.6771 0 Td
(to)Tj
1.0261 0 Td
(contain)Tj
-32.2069 -1.2982 Td
(one)Tj
1.6951 0 Td
(of)Tj
1.0148 0 Td
(these)Tj
2.2564 0 Td
(representative)Tj
5.8335 0 Td
(queries,)Tj
3.3279 0 Td
(potentially)Tj
4.4617 0 Td
(reducing)Tj
3.7757 0 Td
(the)Tj
1.4684 0 Td
(size)Tj
1.6837 0 Td
(of)Tj
1.0148 0 Td
(Bloom)Tj
2.88 0 Td
(filters)Tj
2.4775 0 Td
(that)Tj
1.7744 0 Td
(must)Tj
-33.6639 -1.2983 Td
(be)Tj
1.1509 0 Td
(maintained.)Tj
-1.1566 -1.8992 Td
(Minimizers)Tj
4.8529 0 Td
(have)Tj
2.058 0 Td
(been)Tj
2.1259 0 Td
(used)Tj
2.0579 0 Td
(for)Tj
1.3889 0 Td
(some)Tj
2.3301 0 Td
(of)Tj
1.0148 0 Td
(these)Tj
2.2507 0 Td
(and)Tj
1.7348 0 Td
(similar)Tj
2.982 0 Td
(applications)Tj
5.0457 0 Td
([)Tj
0.83 0.64 0.02 0 k
(4)Tj
0 g
(,)Tj
0.83 0.64 0.02 0 k
1.2585 0 Td
(7)Tj
0 g
()Tj
0.83 0.64 0.02 0 k
(9)Tj
0 g
(].)Tj
2.2564 0 Td
(They)Tj
2.2337 0 Td
(were)Tj
-34.7865 -1.3039 Td
(originally)Tj
4.0252 0 Td
(introduced)Tj
4.6431 0 Td
(by)Tj
1.1792 0 Td
(Roberts)Tj
/F10 1 Tf
3.3108 0 Td
[()8()]TJ
0.9127 0 Td
[()11()]TJ
/F9 1 Tf
(.)Tj
1.1679 0 Td
([)Tj
0.83 0.64 0.02 0 k
(1)Tj
0 g
(])Tj
1.3719 0 Td
(for)Tj
1.389 0 Td
(genome)Tj
3.4072 0 Td
(assembly.)Tj
4.0536 0 Td
(The)Tj
1.7801 0 Td
(same)Tj
2.2564 0 Td
(idea)Tj
1.8765 0 Td
(was)Tj
1.6951 0 Td
(introduced)Tj
-33.0687 -1.2983 Td
(independently)Tj
5.9754 0 Td
(for)Tj
1.3833 0 Td
(plagiarism)Tj
4.4049 0 Td
(detection)Tj
3.9345 0 Td
(in)Tj
1.0375 0 Td
(Schleimer)Tj
/F10 1 Tf
4.2009 0 Td
[()8()]TJ
0.9071 0 Td
[()11()]TJ
/F9 1 Tf
(.)Tj
1.1678 0 Td
([)Tj
0.83 0.64 0.02 0 k
(2)Tj
0 g
(].)Tj
1.6044 0 Td
(For)Tj
1.6214 0 Td
(example,)Tj
3.7758 0 Td
(MSP)Tj
2.1486 0 Td
([)Tj
0.83 0.64 0.02 0 k
(10)Tj
0 g
(])Tj
1.8539 0 Td
(com-)Tj
-34.0155 -1.2982 Td
(presses)Tj
/F10 1 Tf
3.0387 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(by)Tj
1.1792 0 Td
(hashing)Tj
3.3506 0 Td
(them)Tj
2.2902 0 Td
(to)Tj
1.0262 0 Td
(their)Tj
2.1089 0 Td
(4-mer)Tj
2.6589 0 Td
(minimizer)Tj
4.4164 0 Td
(to)Tj
1.0261 0 Td
(efficiently)Tj
4.1499 0 Td
(construct)Tj
3.9798 0 Td
(a)Tj
0.652 0 Td
(de)Tj
1.1735 0 Td
(Bruijn)Tj
-34.0608 -1.3039 Td
(graph)Tj
2.5342 0 Td
(for)Tj
1.389 0 Td
(assembly.)Tj
4.0478 0 Td
(SparseAssembler)Tj
7.0014 0 Td
([)Tj
0.83 0.64 0.02 0 k
(11)Tj
0 g
(])Tj
1.8539 0 Td
(represents)Tj
4.3143 0 Td
(the)Tj
1.474 0 Td
(de)Tj
1.1679 0 Td
(Bruijn)Tj
2.7722 0 Td
(graph)Tj
2.5342 0 Td
(using)Tj
2.3924 0 Td
(only)Tj
1.9786 0 Td
(every)Tj
/F10 1 Tf
2.347 0 Td
[()]TJ
/F9 1 Tf
(-th)Tj
/F10 1 Tf
-35.8069 -1.2983 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6476 0 Td
(in)Tj
1.0374 0 Td
(the)Tj
1.4684 0 Td
(sequence)Tj
3.8607 0 Td
(\(and)Tj
2.0692 0 Td
(has)Tj
1.5421 0 Td
(also)Tj
1.7688 0 Td
(been)Tj
2.1203 0 Td
(implemented)Tj
5.5388 0 Td
(using)Tj
2.3868 0 Td
(minimizers\).)Tj
5.3461 0 Td
(Kraken)Tj
3.1634 0 Td
([)Tj
0.83 0.64 0.02 0 k
(12)Tj
0 g
(])Tj
1.8539 0 Td
(uses)Tj
-34.8035 -1.2983 Td
(minimizers)Tj
4.7792 0 Td
(to)Tj
1.0205 0 Td
(speed)Tj
2.4774 0 Td
(up)Tj
1.2643 0 Td
(database)Tj
3.6395 0 Td
(queries)Tj
3.1011 0 Td
(for)Tj
/F10 1 Tf
1.3833 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(during)Tj
2.931 0 Td
(metagenome)Tj
5.3801 0 Td
(sequence)Tj
3.8608 0 Td
(classifica-)Tj
-32.8476 -1.2982 Td
(tion.)Tj
2.0636 0 Td
(KMC)Tj
2.4492 0 Td
(2)Tj
0.6973 0 Td
([)Tj
0.83 0.64 0.02 0 k
(8)Tj
0 g
(])Tj
1.3776 0 Td
(uses)Tj
1.8935 0 Td
(minimizers)Tj
4.7734 0 Td
(to)Tj
1.0262 0 Td
(cluster)Tj
2.8743 0 Td
(subsequences)Tj
5.6126 0 Td
(for)Tj
1.3889 0 Td
(counting)Tj
/F10 1 Tf
3.8041 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6532 0 Td
(occurrences.)Tj
5.2497 0 Td
(The)Tj
-35.8636 -1.304 Td
(Locally)Tj
3.0671 0 Td
(Consistent)Tj
4.4957 0 Td
(Parsing)Tj
3.2258 0 Td
(\(LCP\))Tj
2.6645 0 Td
([)Tj
0.83 0.64 0.02 0 k
(13)Tj
0 g
(])Tj
1.8481 0 Td
(algorithm)Tj
4.1556 0 Td
(provides)Tj
3.651 0 Td
(the)Tj
1.4683 0 Td
(concept)Tj
3.3619 0 Td
(of)Tj
1.0148 0 Td
(core)Tj
2.3414 0 Td
(substrings)Tj
-31.2942 -1.2982 Td
(which,)Tj
2.8743 0 Td
(like)Tj
1.6555 0 Td
(minimizers,)Tj
5.0002 0 Td
(are)Tj
1.4513 0 Td
(guaranteed)Tj
4.6714 0 Td
(to)Tj
1.0262 0 Td
(be)Tj
1.1508 0 Td
(shared)Tj
2.863 0 Td
(by)Tj
1.1849 0 Td
(long)Tj
1.9842 0 Td
(enough)Tj
3.2202 0 Td
(identical)Tj
3.6566 0 Td
(strings.)Tj
3.1181 0 Td
(SCALCE)Tj
-33.8567 -1.2983 Td
([)Tj
0.83 0.64 0.02 0 k
(14)Tj
0 g
(])Tj
1.8482 0 Td
(uses)Tj
1.8935 0 Td
(core)Tj
1.9446 0 Td
(substrings)Tj
4.2916 0 Td
(to)Tj
1.0261 0 Td
(compress)Tj
4.0024 0 Td
(DNA)Tj
2.3755 0 Td
(sequences.)Tj
-16.1857 -1.3039 Td
(A)Tj
0.9071 0 Td
(small)Tj
2.3244 0 Td
(UHS,)Tj
2.4265 0 Td
(if)Tj
0.7766 0 Td
(it)Tj
0.7824 0 Td
(can)Tj
1.6271 0 Td
(be)Tj
1.1507 0 Td
(found,)Tj
2.846 0 Td
(has)Tj
1.542 0 Td
(a)Tj
0.652 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
1.0148 0 Td
(advantages)Tj
4.6034 0 Td
(over)Tj
1.9729 0 Td
(minimizers)Tj
4.7792 0 Td
(for)Tj
1.3889 0 Td
(these)Tj
-33.4088 -1.2983 Td
(applications:)Tj
0 -1.8992 Td
(1.)Tj
1.2019 0 Td
(The)Tj
1.7802 0 Td
(set)Tj
1.3039 0 Td
(of)Tj
1.0148 0 Td
(minimizers)Tj
4.7792 0 Td
(for)Tj
1.3832 0 Td
(a)Tj
0.6519 0 Td
(given)Tj
2.3811 0 Td
(collection)Tj
4.1102 0 Td
(of)Tj
1.0148 0 Td
(reads)Tj
2.3414 0 Td
(may)Tj
1.9276 0 Td
(be)Tj
1.1508 0 Td
(as)Tj
1.0148 0 Td
(dense)Tj
2.5002 0 Td
(as)Tj
1.0148 0 Td
(the)Tj
1.474 0 Td
(complete)Tj
3.8777 0 Td
(set)Tj
1.304 0 Td
(of)Tj
/F10 1 Tf
-35.0246 -1.2982 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(\(size)Tj
2.0239 0 Td
(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 274.1102 465.8456 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 279.8362 461.4236 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(for)Tj
1.3832 0 Td
(an)Tj
1.2019 0 Td
(alphabet)Tj
/F19 1 Tf
3.6113 0 Td
(S)Tj
/F9 1 Tf
(\),)Tj
1.4457 0 Td
(whereas)Tj
3.4469 0 Td
(we)Tj
1.3266 0 Td
(show)Tj
2.3017 0 Td
(that)Tj
1.7745 0 Td
(we)Tj
1.3323 0 Td
(can)Tj
1.6214 0 Td
(often)Tj
2.2847 0 Td
(generate)Tj
3.6113 0 Td
(UHSs)Tj
-32.1219 -1.3039 Td
(smaller)Tj
3.1181 0 Td
(by)Tj
1.1849 0 Td
(a)Tj
0.6519 0 Td
(factor)Tj
2.5398 0 Td
(of)Tj
1.0148 0 Td
(nearly)Tj
/F10 1 Tf
2.6985 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.9128 0 Td
(We)Tj
1.6101 0 Td
(also)Tj
1.7688 0 Td
(demonstrate)Tj
5.2327 0 Td
(on)Tj
1.2756 0 Td
(real)Tj
1.6951 0 Td
(genomic)Tj
3.6737 0 Td
(sequences)Tj
4.2179 0 Td
(that)Tj
1.7801 0 Td
(the)Tj
-33.3748 -1.2982 Td
(number)Tj
3.4129 0 Td
(of)Tj
1.0148 0 Td
(UHS)Tj
/F10 1 Tf
2.1997 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0159 0 Td
(needed)Tj
3.0898 0 Td
(to)Tj
1.0261 0 Td
(process)Tj
3.1861 0 Td
(them)Tj
2.2904 0 Td
(is)Tj
0.8447 0 Td
(substantially)Tj
5.2044 0 Td
(smaller.)Tj
-26.4867 -1.8992 Td
(2.)Tj
1.2019 0 Td
(For)Tj
1.6214 0 Td
(any)Tj
/F10 1 Tf
1.6611 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(and)Tj
/F10 1 Tf
1.7291 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9695 0 Td
(a)Tj
0.6575 0 Td
(set)Tj
1.3039 0 Td
(of)Tj
1.0148 0 Td
(universal)Tj
/F10 1 Tf
3.8494 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0161 0 Td
(needs)Tj
2.5001 0 Td
(to)Tj
1.0262 0 Td
(be)Tj
1.1508 0 Td
(computed)Tj
4.2633 0 Td
(only)Tj
1.9786 0 Td
(once)Tj
2.1203 0 Td
(and)Tj
1.7348 0 Td
(not)Tj
1.5704 0 Td
(recom-)Tj
-32.8533 -1.2983 Td
(puted)Tj
2.5115 0 Td
(for)Tj
1.389 0 Td
(every)Tj
2.347 0 Td
(dataset.)Tj
-7.4494 -1.9049 Td
(3.)Tj
1.2019 0 Td
(The)Tj
1.7802 0 Td
(hash)Tj
2.0692 0 Td
(buckets,)Tj
3.4865 0 Td
(sparse)Tj
2.6873 0 Td
(suffix)Tj
2.4151 0 Td
(arrays,)Tj
2.8743 0 Td
(and)Tj
1.7291 0 Td
(Bloom)Tj
2.88 0 Td
(filters)Tj
2.4718 0 Td
(created)Tj
3.1237 0 Td
(for)Tj
1.3833 0 Td
(different)Tj
3.6567 0 Td
(datasets)Tj
3.3619 0 Td
(will)Tj
-33.9191 -1.2982 Td
(contain)Tj
3.2428 0 Td
(a)Tj
0.6577 0 Td
(comparable)Tj
4.9038 0 Td
(set)Tj
1.2982 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0161 0 Td
(if)Tj
0.771 0 Td
(they)Tj
1.9275 0 Td
(are)Tj
1.4457 0 Td
(sampled)Tj
3.549 0 Td
(according)Tj
4.1895 0 Td
(to)Tj
1.0262 0 Td
(a)Tj
0.6519 0 Td
(UHS.)Tj
2.4265 0 Td
(This)Tj
1.9842 0 Td
(will)Tj
1.6668 0 Td
(enable)Tj
-33.7717 -1.2983 Td
(easier)Tj
2.5002 0 Td
(comparison)Tj
4.9718 0 Td
(and)Tj
1.7348 0 Td
(integration)Tj
4.6488 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(datasets.)Tj
-17.5406 -1.8992 Td
(4.)Tj
1.2019 0 Td
(One)Tj
1.9389 0 Td
(does)Tj
2.0353 0 Td
(not)Tj
1.576 0 Td
(need)Tj
2.1429 0 Td
(to)Tj
1.0261 0 Td
(look)Tj
1.9729 0 Td
(at)Tj
0.9525 0 Td
(the)Tj
1.474 0 Td
(reads)Tj
2.3357 0 Td
(or)Tj
1.0998 0 Td
(to)Tj
1.0262 0 Td
(build)Tj
2.2904 0 Td
(a)Tj
0.6576 0 Td
(dataset-specific)Tj
6.3155 0 Td
(de)Tj
1.1736 0 Td
(Bruijn)Tj
2.7722 0 Td
(graph)Tj
2.5342 0 Td
(in)Tj
-33.3238 -1.3039 Td
(order)Tj
2.4208 0 Td
(to)Tj
1.0205 0 Td
(decide)Tj
2.8176 0 Td
(which)Tj
/F10 1 Tf
2.6474 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(to)Tj
1.0261 0 Td
(use.)Tj
-12.9484 -1.8992 Td
(Problem)Tj
3.6566 0 Td
(1)Tj
0.6973 0 Td
(can)Tj
1.6214 0 Td
(be)Tj
1.1508 0 Td
(rephrased)Tj
4.1782 0 Td
(as)Tj
1.0148 0 Td
(a)Tj
0.6577 0 Td
(problem)Tj
3.6113 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4683 0 Td
(complete)Tj
3.8778 0 Td
(de)Tj
1.1735 0 Td
(Bruijn)Tj
2.7666 0 Td
(graph)Tj
2.5398 0 Td
(of)Tj
1.0148 0 Td
(order)Tj
/F10 1 Tf
2.4208 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(\(see)Tj
-35.0076 -1.2983 Td
(Definition)Tj
4.371 0 Td
(1)Tj
0.6974 0 Td
(below\).)Tj
3.152 0 Td
(This)Tj
1.9842 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4683 0 Td
(viewpoint)Tj
4.1896 0 Td
(we)Tj
1.3266 0 Td
(take)Tj
1.8709 0 Td
(for)Tj
1.3889 0 Td
(most)Tj
2.2054 0 Td
(of)Tj
1.0148 0 Td
(this)Tj
1.6724 0 Td
(study:)Tj
/F10 1 Tf
-24.9956 -1.2982 Td
[()2()20()13()10()4()2()]TJ
3.4809 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.9071 0 Td
(Given)Tj
2.6304 0 Td
(a)Tj
0.652 0 Td
(de)Tj
1.1735 0 Td
(Bruijn)Tj
2.7723 0 Td
(graph)Tj
/F10 1 Tf
2.5341 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 360.4535 279.7228 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 366.1228 281.4236 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(of)Tj
1.0147 0 Td
(order)Tj
/F10 1 Tf
2.4208 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(and)Tj
1.7291 0 Td
(an)Tj
1.2019 0 Td
(integer)Tj
/F10 1 Tf
3.016 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9752 0 Td
(find)Tj
1.8481 0 Td
(a)Tj
0.6577 0 Td
(smallest)Tj
3.4072 0 Td
(set)Tj
1.3039 0 Td
(of)Tj
1.0148 0 Td
(ver-)Tj
-35.8863 -1.3039 Td
(tices)Tj
/F10 1 Tf
1.9899 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 226.885 266.7401 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 238.1669 268.3842 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(such)Tj
2.0636 0 Td
(that)Tj
1.7744 0 Td
(any)Tj
1.6611 0 Td
(path)Tj
1.9956 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 330.4062 266.7401 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 336.0755 268.3842 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(of)Tj
1.0147 0 Td
(length)Tj
/F17 1 Tf
2.7326 0 Td
[()]TJ
/F9 1 Tf
0.6236 0 Td
(=)Tj
/F10 1 Tf
0.7994 0 Td
[()]TJ
/F17 1 Tf
0.7484 0 Td
[()]TJ
/F10 1 Tf
0.788 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(passes)Tj
2.6758 0 Td
(through)Tj
3.447 0 Td
(at)Tj
0.9524 0 Td
(least)Tj
1.9842 0 Td
(one)Tj
1.6951 0 Td
(vertex)Tj
2.6589 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 561.2031 266.7401 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 570.3307 268.3842 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
-35.8353 -1.2982 Td
(Here)Tj
2.211 0 Td
(and)Tj
1.7291 0 Td
(throughout,)Tj
5.0003 0 Td
(the)Tj
1.474 0 Td
(length)Tj
2.7269 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
0.652 0 Td
(path)Tj
2.0012 0 Td
(is)Tj
0.8447 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()7()10()2()8(\n)]TJ
/F9 1 Tf
2.2451 0 Td
(in)Tj
1.0374 0 Td
(it.)Tj
1.0092 0 Td
(We)Tj
1.61 0 Td
(show)Tj
2.3018 0 Td
(that)Tj
1.7744 0 Td
(the)Tj
-34.7298 -1.44 Td
(related)Tj
2.9423 0 Td
(problem)Tj
3.6113 0 Td
(of)Tj
1.0148 0 Td
(finding)Tj
3.1351 0 Td
(a)Tj
0.652 0 Td
(minimum-size)Tj
/F10 1 Tf
6.1058 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6475 0 Td
(set)Tj
1.304 0 Td
(that)Tj
1.7801 0 Td
(hits)Tj
1.6724 0 Td
(every)Tj
2.3471 0 Td
(string)Tj
2.5342 0 Td
(in)Tj
1.0374 0 Td
(a)Tj
0.652 0 Td
(given)Tj
2.3811 0 Td
(set)Tj
/F18 1 Tf
0 Tc
1.3039 0.2268 Td
(~)Tj
/F10 1 Tf
-0.0057 -0.2268 Td
[( )]TJ
/F9 1 Tf
-0.004 Tc
0.7314 0 Td
(of)Tj
/F10 1 Tf
-35.8467 -1.44 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.8629 0 Td
(strings)Tj
2.8914 0 Td
(is)Tj
0.8504 0 Td
(NP-hard.)Tj
3.9514 0 Td
(This)Tj
1.9899 0 Td
(problem)Tj
3.6114 0 Td
(differs)Tj
2.7439 0 Td
(from)Tj
2.2053 0 Td
(ours,)Tj
2.211 0 Td
(in)Tj
1.0375 0 Td
(that)Tj
1.7801 0 Td
(the)Tj
1.4684 0 Td
(set)Tj
/F18 1 Tf
0 Tc
1.3096 0.2211 Td
(~)Tj
/F10 1 Tf
-0.0057 -0.2211 Td
[( )]TJ
/F9 1 Tf
-0.004 Tc
0.7257 0 Td
(is)Tj
0.8504 0 Td
(part)Tj
1.8425 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(input.)Tj
-34.8092 -1.2983 Td
(However,)Tj
4.0762 0 Td
(the)Tj
1.4683 0 Td
(fact)Tj
1.6668 0 Td
(that)Tj
1.7744 0 Td
(finding)Tj
3.1351 0 Td
(a)Tj
0.652 0 Td
(small)Tj
2.3301 0 Td
(set)Tj
1.2982 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0161 0 Td
(that)Tj
1.7744 0 Td
(hits)Tj
1.6781 0 Td
(every)Tj
2.3471 0 Td
(sequence)Tj
3.8551 0 Td
(in)Tj
1.0375 0 Td
(a)Tj
0.652 0 Td
(particular)Tj
4.1102 0 Td
(data)Tj
-35.8864 -1.3039 Td
(set)Tj
1.3039 0 Td
(is)Tj
0.8447 0 Td
(hard)Tj
2.0806 0 Td
(further)Tj
3.0274 0 Td
(motivates)Tj
4.0876 0 Td
(the)Tj
1.4683 0 Td
(need)Tj
2.143 0 Td
(for)Tj
1.3833 0 Td
(a)Tj
0.6576 0 Td
(universal)Tj
3.8551 0 Td
(set)Tj
1.2983 0 Td
(that)Tj
1.7801 0 Td
(can)Tj
1.6271 0 Td
(be)Tj
1.1508 0 Td
(computed)Tj
4.2633 0 Td
(once)Tj
2.1203 0 Td
(for)Tj
1.389 0 Td
(any)Tj
-34.4804 -1.2982 Td
(input)Tj
2.3754 0 Td
(sequence.)Tj
4.0875 0 Td
(Our)Tj
1.8652 0 Td
(main)Tj
2.2904 0 Td
(contribution)Tj
5.2894 0 Td
(is)Tj
0.8504 0 Td
(an)Tj
1.2019 0 Td
(algorithm)Tj
4.1555 0 Td
(called)Tj
2.5229 0 Td
(DOCKS)Tj
3.5149 0 Td
(that)Tj
1.7745 0 Td
(finds)Tj
2.2167 0 Td
(a)Tj
0.6519 0 Td
(compact)Tj
3.6453 0 Td
(set)Tj
-36.4419 -1.2983 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0103 0 Td
(that)Tj
1.7802 0 Td
(hits)Tj
1.6724 0 Td
(any)Tj
/F10 1 Tf
1.6554 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.8687 0 Td
(sequence.)Tj
4.0819 0 Td
(We)Tj
1.61 0 Td
(also)Tj
1.7688 0 Td
(provide)Tj
3.2882 0 Td
(several)Tj
2.931 0 Td
(variants)Tj
3.3902 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(algorithm,)Tj
-31.555 -1.3039 Td
(trading-off)Tj
4.5637 0 Td
(some)Tj
2.3301 0 Td
(solution)Tj
3.4866 0 Td
(quality)Tj
2.9537 0 Td
(for)Tj
1.3833 0 Td
(speed.)Tj
2.6985 0 Td
(We)Tj
1.6101 0 Td
(show)Tj
2.3017 0 Td
(empirically)Tj
4.6885 0 Td
(that)Tj
1.7801 0 Td
(the)Tj
1.4684 0 Td
(produced)Tj
4.0478 0 Td
(sets)Tj
1.6611 0 Td
(are)Tj
-34.9736 -1.2983 Td
(often)Tj
2.2847 0 Td
(close)Tj
2.1826 0 Td
(to)Tj
1.0205 0 Td
(a)Tj
0.6576 0 Td
(theoretical)Tj
4.4391 0 Td
(lower)Tj
2.4548 0 Td
(bound,)Tj
3.0614 0 Td
(implying)Tj
3.804 0 Td
(their)Tj
2.109 0 Td
(near-optimality.)Tj
6.684 0 Td
(Our)Tj
1.8652 0 Td
(use)Tj
1.5307 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
0.6577 0 Td
(greedy)Tj
-33.7661 -1.2982 Td
(heuristic)Tj
3.685 0 Td
(is)Tj
0.8504 0 Td
(motivated)Tj
4.2462 0 Td
(by)Tj
1.1849 0 Td
(the)Tj
1.4684 0 Td
(fact)Tj
1.6667 0 Td
(that)Tj
1.7745 0 Td
(finding)Tj
3.1351 0 Td
(a)Tj
0.652 0 Td
(minimum-size)Tj
/F17 1 Tf
6.1058 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.7382 0 Td
(path)Tj
2.0012 0 Td
(cover)Tj
2.3981 0 Td
(in)Tj
1.0375 0 Td
(a)Tj
0.652 0 Td
(graph)Tj
/F10 1 Tf
2.5341 0 Td
[()]TJ
/F9 1 Tf
-36.1301 -1.304 Td
(is)Tj
0.8447 0 Td
(NP-hard)Tj
3.7304 0 Td
(when)Tj
/F10 1 Tf
2.4037 0 Td
[()]TJ
/F9 1 Tf
0.8901 0 Td
(is)Tj
0.8504 0 Td
(a)Tj
0.652 0 Td
(directed)Tj
3.4865 0 Td
(acyclic)Tj
2.8914 0 Td
(graph)Tj
2.5341 0 Td
(\(DAG\).)Tj
3.2598 0 Td
(We)Tj
1.6101 0 Td
(report)Tj
2.7099 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4683 0 Td
(size)Tj
1.6838 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.474 0 Td
(universal)Tj
/F10 1 Tf
-32.7796 -1.2982 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6475 0 Td
(hitting)Tj
2.8913 0 Td
(set)Tj
1.304 0 Td
(produced)Tj
4.0478 0 Td
(by)Tj
1.1792 0 Td
(DOCKS)Tj
3.515 0 Td
(and)Tj
1.7347 0 Td
(demonstrate)Tj
5.2328 0 Td
(on)Tj
1.2756 0 Td
(genomic)Tj
3.6736 0 Td
(datasets)Tj
3.3562 0 Td
(that)Tj
1.7802 0 Td
(we)Tj
1.3266 0 Td
(can)Tj
-33.9645 -1.2983 Td
(more)Tj
2.3414 0 Td
(uniformly)Tj
4.2462 0 Td
(cover)Tj
2.4038 0 Td
(sequences)Tj
4.2179 0 Td
(with)Tj
1.9956 0 Td
(a)Tj
0.6576 0 Td
(smaller)Tj
3.1181 0 Td
(set)Tj
1.304 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0103 0 Td
(than)Tj
2.0296 0 Td
(is)Tj
0.8504 0 Td
(possible)Tj
3.4072 0 Td
(using)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 169.285 23.6976 re
W* n
q
169.2283 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 450.4818 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Compact)Tj
4.1669 0 Td
(universal)Tj
/F7 1 Tf
4.1386 0 Td
(k)Tj
/F0 1 Tf
(-mer)Tj
2.7355 0 Td
(hitting)Tj
2.8346 0 Td
(sets)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
142.5827 34.9228 m
295.8236 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(Computationa)Tj
6.1229 0 Td
(l)Tj
0.4322 0 Td
(Biology)Tj
3.4371 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https:/)Tj
2.6788 0 Td
(/doi.org/10.13)Tj
6.0094 0 Td
(71/journal.p)Tj
5.1166 0 Td
(cbi.1005777)Tj
0 g
6.3497 0 Td
(October)Tj
3.7276 0 Td
(2,)Tj
1.0346 0 Td
(2017)Tj
26.901 0 Td
(3)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
54 0 obj
<>stream
endstream
endobj
55 0 obj
<>stream
endstream
endobj
56 0 obj
<>stream
endstream
endobj
57 0 obj
<>stream
endstream
endobj
58 0 obj
<>stream
endstream
endobj
59 0 obj
<>stream
endstream
endobj
60 0 obj
<>stream
endstream
endobj
61 0 obj
<>stream
endstream
endobj
62 0 obj
<>stream
endstream
endobj
63 0 obj
<>stream
endstream
endobj
64 0 obj
<>stream
BT
66.402 0 Td
(15)Tj
ET
Q
endstream
endobj
65 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 17 0 R/Annots 67 0 R/Contents 68 0 R/TrimBox[0 0 612 792]>>
endobj
67 0 obj
[69 0 R 70 0 R 71 0 R 72 0 R 73 0 R 74 0 R 75 0 R 76 0 R 77 0 R 78 0 R]
endobj
69 0 obj
<>/Border[0 0 0]/A 79 0 R>>
endobj
79 0 obj
<>
endobj
70 0 obj
<>/Border[0 0 0]/A 80 0 R>>
endobj
80 0 obj
<>
endobj
71 0 obj
<>/Border[0 0 0]/A 81 0 R>>
endobj
81 0 obj
<>
endobj
72 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref015)>>
endobj
73 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.s002)>>
endobj
74 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref016)>>
endobj
75 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref016)>>
endobj
76 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref017)>>
endobj
77 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.e016)>>
endobj
78 0 obj
<>/Border[0 0 0]/A 82 0 R>>
endobj
82 0 obj
<>
endobj
68 0 obj
[83 0 R 84 0 R 85 0 R 86 0 R 87 0 R 88 0 R 89 0 R 90 0 R 91 0 R]
endobj
83 0 obj
<>stream
q
0.83 0.64 0.02 0 k
441.1276 680.315 m
540.6803 680.315 l
h
f*
200.0126 667.3323 m
236.2394 667.3323 l
h
f*
270.4819 654.3496 m
359.6031 654.3496 l
h
f*
557.2346 654.3496 m
566.7591 654.3496 l
h
f*
271.8425 271.3323 m
301.1528 271.3323 l
h
f*
448.2709 159.9307 m
457.7386 159.9307 l
h
f*
304.6677 133.9087 m
314.1921 133.9087 l
h
f*
503.5465 133.9087 m
513.0709 133.9087 l
h
f*
340.2142 107.9433 m
362.7213 107.9433 l
h
f*
0 g
1 j
1 J
0 w
10 0 0 10 200.0125 707.4141 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(minimizers.)Tj
5.0002 0 Td
(For)Tj
1.6271 0 Td
(example,)Tj
3.7757 0 Td
(we)Tj
1.3266 0 Td
(show)Tj
2.3018 0 Td
(that)Tj
1.7744 0 Td
(the)Tj
1.474 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(needed)Tj
3.0954 0 Td
(to)Tj
1.0205 0 Td
(cover)Tj
2.4037 0 Td
(the)Tj
1.4684 0 Td
(human)Tj
-32.7116 -1.3039 Td
(genome)Tj
3.4072 0 Td
(using)Tj
2.3867 0 Td
(a)Tj
0.6577 0 Td
(UHS)Tj
2.1996 0 Td
(is)Tj
0.8448 0 Td
(less)Tj
1.61 0 Td
(than)Tj
2.0296 0 Td
(one)Tj
1.7008 0 Td
(third)Tj
2.211 0 Td
(of)Tj
1.0148 0 Td
(that)Tj
1.7801 0 Td
(required)Tj
3.6397 0 Td
(by)Tj
1.1792 0 Td
(minimizers.)Tj
-23.465 -1.2982 Td
(The)Tj
1.7858 0 Td
(software)Tj
3.5886 0 Td
(to)Tj
1.0205 0 Td
(compute)Tj
3.7417 0 Td
(small)Tj
2.3244 0 Td
(UHSs)Tj
2.5625 0 Td
(is)Tj
0.8447 0 Td
(freely)Tj
2.4265 0 Td
(available)Tj
3.668 0 Td
(at)Tj
0.83 0.64 0.02 0 k
0.9524 0 Td
(github.com/Shamir-Lab)Tj
9.6264 0 Td
(/)Tj
-33.7377 -1.2983 Td
(DOCKS/)Tj
0 g
(.)Tj
4.0705 0 Td
(Universal)Tj
4.0592 0 Td
(sets)Tj
1.6667 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(computed)Tj
4.2633 0 Td
(by)Tj
1.1848 0 Td
(DOCKS)Tj
3.515 0 Td
(for)Tj
1.3833 0 Td
(a)Tj
0.6576 0 Td
(range)Tj
2.4605 0 Td
(of)Tj
1.0148 0 Td
(values)Tj
2.6702 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
0.7427 0 Td
(and)Tj
/F10 1 Tf
1.7348 0 Td
[()]TJ
/F9 1 Tf
0.6803 0 Td
(are)Tj
-35.1437 -1.2983 Td
(freely)Tj
2.4264 0 Td
(available)Tj
3.668 0 Td
(at)Tj
0.83 0.64 0.02 0 k
0.9524 0 Td
(acgt.cs.tau.ac.il/docks/)Tj
0 g
(.)Tj
9.3543 0 Td
(A)Tj
0.9071 0 Td
(preliminary)Tj
4.9379 0 Td
(version)Tj
3.1521 0 Td
(of)Tj
1.0148 0 Td
(this)Tj
1.6781 0 Td
(study)Tj
2.3868 0 Td
(appeared)Tj
3.8721 0 Td
(in)Tj
1.0318 0 Td
([)Tj
0.83 0.64 0.02 0 k
(15)Tj
0 g
(].)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 626.0031 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(Preliminaries)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 608.9952 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(Throughout)Tj
5.0909 0 Td
(this)Tj
1.6725 0 Td
(paper,)Tj
/F10 1 Tf
2.7099 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(denotes)Tj
3.3051 0 Td
(the)Tj
1.474 0 Td
(length)Tj
2.727 0 Td
(of)Tj
1.0147 0 Td
(a)Tj
/F10 1 Tf
0.6577 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6475 0 Td
(word,)Tj
2.5342 0 Td
(while)Tj
/F10 1 Tf
2.3697 0 Td
[()]TJ
/F9 1 Tf
0.7484 0 Td
(denotes)Tj
3.3108 0 Td
(the)Tj
1.4684 0 Td
(length)Tj
2.7269 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
-36.1585 -1.2982 Td
(long)Tj
1.9842 0 Td
(sequences.)Tj
/F16 1 Tf
-0.788 -1.3039 Td
(Definition)Tj
4.5807 0 Td
(1)Tj
0.72 0 Td
(\(de)Tj
1.5534 0 Td
(Bruijn)Tj
2.9367 0 Td
(Graph\).)Tj
/F9 1 Tf
3.5092 0 Td
(A)Tj
/F10 1 Tf
0.9014 0 Td
[()4()]TJ
1.1112 0 Td
[()17()-9(\r)12()12()14()]TJ
2.7269 0 Td
[()-8()20()12()10()]TJ
/F9 1 Tf
2.4605 0 Td
(of)Tj
1.0148 0 Td
(order)Tj
/F10 1 Tf
2.4264 0 Td
[()]TJ
/F9 1 Tf
0.6803 0 Td
(over)Tj
1.9786 0 Td
(alphabet)Tj
/F19 1 Tf
3.6057 0 Td
(S)Tj
/F9 1 Tf
0.8844 0 Td
(is)Tj
0.8503 0 Td
(a)Tj
0.652 0 Td
(directed)Tj
-33.7887 -1.2983 Td
(graph)Tj
2.5341 0 Td
(in)Tj
1.0375 0 Td
(which)Tj
2.6475 0 Td
(every)Tj
2.3471 0 Td
(vertex)Tj
2.6589 0 Td
(has)Tj
1.542 0 Td
(an)Tj
1.2019 0 Td
(associated)Tj
4.2576 0 Td
(label)Tj
2.075 0 Td
(\(a)Tj
0.9977 0 Td
(string)Tj
2.5285 0 Td
(over)Tj
/F19 1 Tf
1.9786 0 Td
(S)Tj
/F9 1 Tf
(\))Tj
1.2246 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7269 0 Td
[()]TJ
/F9 1 Tf
0.6859 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(-mer\))Tj
3.3279 0 Td
(and)Tj
-34.7865 -1.2983 Td
(every)Tj
2.347 0 Td
(edge)Tj
2.058 0 Td
(has)Tj
1.542 0 Td
(an)Tj
1.2019 0 Td
(associated)Tj
4.2576 0 Td
(label)Tj
2.0806 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7269 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(+)Tj
0.7994 0 Td
(1.)Tj
0.9241 0 Td
(There)Tj
2.5738 0 Td
(are)Tj
1.4513 0 Td
(exactly)Tj
2.965 0 Td
(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 478.0346 561.4299 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 483.7606 557.0078 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(vertices)Tj
3.2428 0 Td
(in)Tj
1.0318 0 Td
(a)Tj
0.6576 0 Td
(de)Tj
1.1679 0 Td
(Bruijn)Tj
-34.4747 -1.3039 Td
(graph,)Tj
2.761 0 Td
(each)Tj
2.0295 0 Td
(representing)Tj
5.2384 0 Td
(a)Tj
0.652 0 Td
(unique)Tj
/F10 1 Tf
3.0217 0 Td
[()]TJ
/F9 1 Tf
(-mer.)Tj
2.8743 0 Td
(If)Tj
0.8504 0 Td
(an)Tj
1.2019 0 Td
(edge)Tj
2.0579 0 Td
(\()Tj
/F10 1 Tf
[(\r)]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.3153 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
0.9921 0 Td
(has)Tj
1.5421 0 Td
(label)Tj
/F10 1 Tf
2.0806 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.6803 0 Td
(then)Tj
2.0181 0 Td
(the)Tj
1.4684 0 Td
(label)Tj
2.0749 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[(\r)]TJ
/F9 1 Tf
0.7484 0 Td
(must)Tj
-34.6221 -1.2982 Td
(be)Tj
1.1509 0 Td
(the)Tj
/F10 1 Tf
1.4683 0 Td
[()]TJ
/F9 1 Tf
(-prefix)Tj
3.3676 0 Td
(\(prefix)Tj
2.8913 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7326 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
1.0261 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
0.4535 0 Td
(and)Tj
1.7292 0 Td
(the)Tj
1.4683 0 Td
(label)Tj
2.0806 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
0.652 0 Td
(must)Tj
2.228 0 Td
(be)Tj
1.1508 0 Td
(the)Tj
/F10 1 Tf
1.4684 0 Td
[()]TJ
/F9 1 Tf
(-suffix)Tj
3.2314 0 Td
(\(suffix)Tj
2.7552 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7326 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
-36.646 -1.2983 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.6803 0 Td
(A)Tj
/F10 1 Tf
0.9014 0 Td
[( )7()11()15()10()4()8()11()]TJ
/F9 1 Tf
3.6284 0 Td
(de)Tj
1.1735 0 Td
(Bruijn)Tj
2.7723 0 Td
(graph)Tj
2.5341 0 Td
(contains)Tj
3.6113 0 Td
(all)Tj
1.1452 0 Td
(possible)Tj
3.4073 0 Td
(edges)Tj
2.4207 0 Td
(of)Tj
1.0148 0 Td
(this)Tj
1.6781 0 Td
(type,)Tj
2.1373 0 Td
(which)Tj
2.6475 0 Td
(represent)Tj
-30.767 -1.3039 Td
(together)Tj
3.532 0 Td
(all)Tj
1.1508 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
1.0205 0 Td
(+)Tj
0.7994 0 Td
(1\)-mers)Tj
3.3618 0 Td
(over)Tj
/F19 1 Tf
1.9786 0 Td
(S)Tj
/F9 1 Tf
(.)Tj
-10.6469 -1.2983 Td
(Every)Tj
2.4945 0 Td
(path)Tj
2.0013 0 Td
(in)Tj
1.0318 0 Td
(a)Tj
0.6576 0 Td
(de)Tj
1.1679 0 Td
(Bruijn)Tj
2.7722 0 Td
(graph)Tj
2.5342 0 Td
(represents)Tj
4.32 0 Td
(a)Tj
0.6576 0 Td
(sequence.)Tj
4.0819 0 Td
(A)Tj
0.9014 0 Td
(path)Tj
/F10 1 Tf
2.0012 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 462.5007 490.337 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 466.0724 491.9811 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
/F10 1 Tf
0.4478 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 474.4629 490.337 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 477.9779 491.9811 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
/F10 1 Tf
0.4478 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 486.822 490.337 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 490.337 491.9811 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
/F10 1 Tf
0.4478 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 498.7275 490.337 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 502.2992 491.9811 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
/F10 1 Tf
0.4422 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 511.0866 490.337 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(2)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 514.6582 491.9811 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
/F18 1 Tf
0 Tc
0.4422 0 Td
(.)Tj
0.4365 0 Td
(.)Tj
0.4308 0 Td
(.)Tj
/F9 1 Tf
-0.004 Tc
(,)Tj
/F10 1 Tf
0.72 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 539.2629 490.337 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 545.4425 491.9811 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(of)Tj
-34.5427 -1.2982 Td
(length)Tj
/F10 1 Tf
2.7269 0 Td
[()]TJ
/F9 1 Tf
0.7483 0 Td
(spells)Tj
2.3754 0 Td
(a)Tj
0.652 0 Td
(sequence)Tj
/F10 1 Tf
3.8608 0 Td
[(\n)]TJ
/F9 1 Tf
0.5499 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7269 0 Td
[()]TJ
/F9 1 Tf
0.7483 0 Td
(+)Tj
/F10 1 Tf
0.7994 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(such)Tj
2.0636 0 Td
(that)Tj
1.7745 0 Td
(the)Tj
1.474 0 Td
(label)Tj
2.0749 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 457.2283 477.2976 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 461.4236 478.9984 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(occurs)Tj
2.8346 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[(\n)]TJ
/F9 1 Tf
0.5499 0 Td
(starting)Tj
3.2655 0 Td
(at)Tj
0.9524 0 Td
(posi-)Tj
-34.7808 -1.2982 Td
(tion)Tj
/F10 1 Tf
1.8425 0 Td
[()]TJ
/F9 1 Tf
0.4819 0 Td
(for)Tj
1.389 0 Td
(all)Tj
1.1452 0 Td
(0)Tj
/F15 1 Tf
0 Tc
0.6973 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.4876 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9694 0 Td
(and)Tj
1.7291 0 Td
(the)Tj
1.4741 0 Td
(label)Tj
2.0749 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 356.8251 464.3149 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 361.0204 466.0157 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(occurs)Tj
2.8346 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[(\n)]TJ
/F9 1 Tf
0.5499 0 Td
(starting)Tj
3.2598 0 Td
(at)Tj
0.9524 0 Td
(position)Tj
/F10 1 Tf
3.4923 0 Td
[()]TJ
/F9 1 Tf
0.4875 0 Td
(for)Tj
1.389 0 Td
(all)Tj
1.1452 0 Td
(0)Tj
/F15 1 Tf
0 Tc
0.6973 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.4876 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F17 1 Tf
0.7427 0 Td
[()]TJ
/F9 1 Tf
0.7937 0 Td
(1.)Tj
-35.9543 -1.3039 Td
(Note)Tj
2.1826 0 Td
(that)Tj
1.7802 0 Td
(vertices)Tj
3.2428 0 Td
(and)Tj
1.7291 0 Td
(edges)Tj
2.4208 0 Td
(may)Tj
1.9275 0 Td
(repeat)Tj
2.6873 0 Td
(in)Tj
1.0373 0 Td
(a)Tj
0.652 0 Td
(path.)Tj
-16.4634 -1.2982 Td
(We)Tj
1.61 0 Td
(define)Tj
2.6986 0 Td
(terminology)Tj
5.1307 0 Td
(for)Tj
/F10 1 Tf
1.3833 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.016 0 Td
(intersecting)Tj
4.9152 0 Td
(sequences)Tj
4.2179 0 Td
(over)Tj
1.9786 0 Td
(an)Tj
1.2019 0 Td
(alphabet)Tj
/F19 1 Tf
3.6056 0 Td
(S)Tj
/F9 1 Tf
(:)Tj
/F16 1 Tf
-29.7578 -1.2983 Td
(Definition)Tj
4.5807 0 Td
(2)Tj
0.72 0 Td
(\(hits\).)Tj
/F9 1 Tf
2.7213 0 Td
(We)Tj
1.61 0 Td
(say)Tj
1.474 0 Td
(that)Tj
/F10 1 Tf
1.7745 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
/F10 1 Tf
2.6531 0 Td
[(!)]TJ
0.8788 0 Td
[()18()14(\n)]TJ
/F9 1 Tf
1.627 0 Td
(string)Tj
/F10 1 Tf
2.5285 0 Td
[( )]TJ
/F9 1 Tf
(,)Tj
0.9014 0 Td
(denoted)Tj
/F10 1 Tf
3.4753 0 Td
[(!)]TJ
/F15 1 Tf
0 Tc
0.8844 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[( )]TJ
/F9 1 Tf
(,)Tj
0.9014 0 Td
(if)Tj
/F10 1 Tf
0.7711 0 Td
[(!)]TJ
/F9 1 Tf
0.8844 0 Td
(appears)Tj
3.2768 0 Td
(as)Tj
1.0148 0 Td
(a)Tj
-34.8658 -1.3039 Td
(contiguous)Tj
4.6544 0 Td
(substring)Tj
3.9231 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[( )]TJ
/F9 1 Tf
(.)Tj
/F10 1 Tf
0.9014 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6476 0 Td
(set)Tj
/F10 1 Tf
1.3039 0 Td
[(")]TJ
0.8504 0 Td
[()18()14(\n)]TJ
/F9 1 Tf
1.6213 0 Td
(string)Tj
/F10 1 Tf
2.5342 0 Td
[( )]TJ
/F9 1 Tf
0.6746 0 Td
(if)Tj
0.7767 0 Td
(there)Tj
2.262 0 Td
(exists)Tj
/F10 1 Tf
2.3981 0 Td
[(!)]TJ
/F15 1 Tf
0 Tc
0.8787 0 Td
(2)Tj
/F10 1 Tf
-0.004 Tc
0.8788 0 Td
[(")]TJ
/F9 1 Tf
0.8504 0 Td
(s.t.)Tj
/F10 1 Tf
1.3322 0 Td
[(!)]TJ
/F15 1 Tf
0 Tc
0.8845 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[( )]TJ
/F9 1 Tf
(.)Tj
0.9014 0 Td
(Define)Tj
/F10 1 Tf
-32.3033 -1.2983 Td
[()18()14()]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[(!)]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
2.5171 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
1.0885 0 Td
(=)Tj
0.7994 0 Td
({)Tj
/F10 1 Tf
[( )]TJ
/F15 1 Tf
0 Tc
1.0148 0 Td
(2)Tj
/F19 1 Tf
-0.004 Tc
0.8787 0 Td
(S)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 269.6314 405.411 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 275.811 400.9889 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(j)Tj
/F10 1 Tf
-0.004 Tc
0.4875 0 Td
[(!)]TJ
/F15 1 Tf
0 Tc
0.8844 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[( )]TJ
/F9 1 Tf
(})Tj
1.0148 0 Td
(for)Tj
/F10 1 Tf
1.3833 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
/F10 1 Tf
2.6532 0 Td
[(!)]TJ
/F9 1 Tf
0.8844 0 Td
(and)Tj
1.7292 0 Td
(length)Tj
/F10 1 Tf
2.7269 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9751 0 Td
(where)Tj
/F19 1 Tf
2.6475 0 Td
(S)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 446.2299 405.411 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 452.4094 400.9889 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8503 0 Td
(the)Tj
1.4684 0 Td
(set)Tj
1.3039 0 Td
(of)Tj
1.0148 0 Td
(all)Tj
/F10 1 Tf
1.1452 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.863 0 Td
(sub-)Tj
-33.8851 -1.2982 Td
(strings)Tj
2.8913 0 Td
(over)Tj
1.9786 0 Td
(alphabet)Tj
/F19 1 Tf
3.6057 0 Td
(S)Tj
/F9 1 Tf
(.)Tj
1.1111 0 Td
(Define)Tj
/F10 1 Tf
0 Tc
2.9027 0 Td
[()18()14()]TJ
/F15 1 Tf
1.1168 0 Td
()Tj
/F10 1 Tf
[(")]TJ
/F20 1 Tf
1.0772 0 Td
(;)Tj
/F10 1 Tf
0.4365 0 Td
[()]TJ
/F15 1 Tf
()Tj
1.1906 0 Td
()Tj
1.0488 0 Td
([)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 370.7149 381.4866 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[(!)]TJ
/F15 1 Tf
(2)Tj
/F10 1 Tf
[(")]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 383.244 388.0062 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()18()14()]TJ
/F15 1 Tf
1.1225 0 Td
()Tj
/F10 1 Tf
[(!)]TJ
/F20 1 Tf
(;)Tj
/F10 1 Tf
1.491 0 Td
[()]TJ
/F15 1 Tf
()Tj
/F9 1 Tf
-0.004 Tc
(.)Tj
-19.7403 -1.7177 Td
(The)Tj
1.7858 0 Td
(universal)Tj
3.8551 0 Td
(set)Tj
1.2983 0 Td
(of)Tj
1.0148 0 Td
(hitting)Tj
/F10 1 Tf
2.897 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(from)Tj
2.2053 0 Td
(Problem)Tj
3.6509 0 Td
(1)Tj
0.6973 0 Td
(is)Tj
0.8504 0 Td
(then)Tj
2.0183 0 Td
(a)Tj
0.6519 0 Td
(set)Tj
/F10 1 Tf
1.304 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 471.2881 369.1275 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 482.6267 370.8283 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(which)Tj
2.6475 0 Td
(satisfies)Tj
/F10 1 Tf
-30.9087 -1.2982 Td
[()18()14()]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 221.0456 356.1448 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 230.1732 357.8456 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
/F10 1 Tf
0.4478 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
1.0885 0 Td
(=)Tj
/F19 1 Tf
0.7994 0 Td
(S)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 260.1637 362.2677 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 264.0755 357.8456 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 328.422 cm
BT
/F3 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(Materials)Tj
4.5071 0 Td
(and)Tj
1.989 0 Td
(methods)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 311.4141 cm
BT
/F9 1 Tf
1 TL
-0.0099 Tc
0 0 Td
(It)Tj
0.8447 0 Td
(is)Tj
0.839 0 Td
(not)Tj
1.5534 0 Td
(known)Tj
2.9764 0 Td
(how)Tj
1.9218 0 Td
(to)Tj
1.0148 0 Td
(efficiently)Tj
4.0819 0 Td
(find)Tj
1.8255 0 Td
(a)Tj
0.652 0 Td
(minimum)Tj
4.2462 0 Td
(universal)Tj
3.7984 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.2359 0 Td
[()]TJ
/F9 1 Tf
(\)-hitting)Tj
4.0535 0 Td
(set.)Tj
1.5024 0 Td
(As)Tj
1.2529 0 Td
(we)Tj
1.3153 0 Td
(prove)Tj
2.4661 0 Td
(in)Tj
-35.5802 -1.2982 Td
(the)Tj
1.4513 0 Td
(Appendix,)Tj
4.3426 0 Td
(the)Tj
1.4514 0 Td
(problem)Tj
3.5716 0 Td
(of)Tj
1.0034 0 Td
(finding)Tj
3.0898 0 Td
(a)Tj
0.6463 0 Td
(minimum)Tj
4.2519 0 Td
(\(non-universal\))Tj
/F10 1 Tf
6.4006 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6192 0 Td
(set)Tj
1.2869 0 Td
(that)Tj
1.7518 0 Td
(hits)Tj
1.6498 0 Td
(a)Tj
0.652 0 Td
(given)Tj
2.347 0 Td
(set)Tj
-36.5156 -1.3039 Td
(of)Tj
1.0034 0 Td
(input)Tj
2.3471 0 Td
(sequences)Tj
4.1669 0 Td
(is)Tj
0.839 0 Td
(NP-hard)Tj
3.685 0 Td
(\(see)Tj
1.7405 0 Td
(Appendix,)Tj
4.3427 0 Td
(Subsection)Tj
4.5013 0 Td
(NP-hardness)Tj
5.3575 0 Td
(of)Tj
1.0035 0 Td
(MINIMUM)Tj
5.0059 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.2359 0 Td
[()]TJ
/F9 1 Tf
(\)-)Tj
-35.2287 -1.2983 Td
(HITTING)Tj
4.2972 0 Td
(SET)Tj
1.8596 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0261 0 Td
(S1)Tj
1.1565 0 Td
(Text)Tj
0 g
(\).)Tj
2.5512 0 Td
(In)Tj
1.0942 0 Td
(the)Tj
1.4513 0 Td
(face)Tj
1.7688 0 Td
(of)Tj
1.0035 0 Td
(the)Tj
1.4513 0 Td
(hardness)Tj
3.7247 0 Td
(result)Tj
2.4151 0 Td
(for)Tj
1.3663 0 Td
(this)Tj
1.6497 0 Td
(related)Tj
2.9084 0 Td
(problem,)Tj
3.787 0 Td
(we)Tj
1.3153 0 Td
(give)Tj
-34.8262 -1.2983 Td
(below)Tj
2.5568 0 Td
(a)Tj
0.6463 0 Td
(practical)Tj
3.5829 0 Td
(heuristic)Tj
3.634 0 Td
(to)Tj
1.0148 0 Td
(find)Tj
1.8255 0 Td
(a)Tj
0.652 0 Td
(compact)Tj
3.6 0 Td
(\(near-optimal\))Tj
6.0377 0 Td
(universal)Tj
/F10 1 Tf
3.7984 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6192 0 Td
(set.)Tj
1.5081 0 Td
(This)Tj
1.9615 0 Td
(algorithm)Tj
-33.4372 -1.3039 Td
(works)Tj
2.6078 0 Td
(on)Tj
1.2643 0 Td
(the)Tj
1.4513 0 Td
(de)Tj
1.1622 0 Td
(Bruijn)Tj
2.7326 0 Td
(graph)Tj
2.5058 0 Td
(of)Tj
1.0034 0 Td
(order)Tj
/F10 1 Tf
2.3925 0 Td
[()]TJ
/F9 1 Tf
0.6803 0 Td
(in)Tj
1.0261 0 Td
(two)Tj
1.6894 0 Td
(steps:)Tj
2.3698 0 Td
(first)Tj
1.7745 0 Td
(it)Tj
0.7767 0 Td
(finds)Tj
2.1826 0 Td
(and)Tj
1.7121 0 Td
(removes)Tj
3.5376 0 Td
(a)Tj
0.652 0 Td
(minimum-size)Tj
/F10 1 Tf
-31.521 -1.2982 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6191 0 Td
(set)Tj
1.287 0 Td
(hitting)Tj
2.8516 0 Td
(all)Tj
1.1282 0 Td
(infinite)Tj
3.0784 0 Td
(sequences,)Tj
4.388 0 Td
(and)Tj
1.7121 0 Td
(then)Tj
1.9956 0 Td
(it)Tj
0.771 0 Td
(finds)Tj
2.1827 0 Td
(and)Tj
1.7121 0 Td
(removes)Tj
3.5433 0 Td
(additional)Tj
/F10 1 Tf
4.2179 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
2.9764 0 Td
(in)Tj
-34.4634 -1.2983 Td
(order)Tj
2.3924 0 Td
(to)Tj
1.0091 0 Td
(hit)Tj
1.2983 0 Td
(all)Tj
1.1281 0 Td
(remaining)Tj
/F10 1 Tf
4.3143 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.829 0 Td
(sequences.)Tj
4.3823 0 Td
(We)Tj
1.5988 0 Td
(now)Tj
1.9445 0 Td
(describe)Tj
3.4753 0 Td
(these)Tj
2.2223 0 Td
(two)Tj
1.6951 0 Td
(steps)Tj
2.1487 0 Td
(in)Tj
1.0261 0 Td
(detail.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 190.9984 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(Finding)Tj
3.4535 0 Td
(a)Tj
0.7701 0 Td
(minimum)Tj
/F7 1 Tf
4.2331 0 Td
(k)Tj
/F0 1 Tf
(-mer)Tj
2.7544 0 Td
(set)Tj
1.5401 0 Td
(hitting)Tj
2.8489 0 Td
(all)Tj
1.2 0 Td
(infinite)Tj
3.0661 0 Td
(sequences)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 173.9905 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(The)Tj
1.7801 0 Td
(problem)Tj
3.6113 0 Td
(of)Tj
1.0148 0 Td
(finding)Tj
3.1351 0 Td
(a)Tj
0.652 0 Td
(minimum-size)Tj
/F10 1 Tf
6.1058 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6475 0 Td
(set)Tj
1.3039 0 Td
(hitting)Tj
2.8914 0 Td
(all)Tj
1.1508 0 Td
(infinite)Tj
3.1238 0 Td
(sequences)Tj
4.2236 0 Td
(is)Tj
0.8447 0 Td
(known)Tj
3.0047 0 Td
(in)Tj
-35.4895 -1.2982 Td
(the)Tj
1.4683 0 Td
(literature)Tj
3.8834 0 Td
(as)Tj
1.0148 0 Td
(finding)Tj
3.1295 0 Td
(an)Tj
1.2018 0 Td
(unavoidable)Tj
5.0967 0 Td
(set)Tj
1.3039 0 Td
(of)Tj
1.0148 0 Td
(constant)Tj
3.6397 0 Td
(length)Tj
2.7326 0 Td
([)Tj
0.83 0.64 0.02 0 k
(16)Tj
0 g
(].)Tj
2.0749 0 Td
(Note)Tj
2.1827 0 Td
(that)Tj
1.7801 0 Td
(finite)Tj
2.3131 0 Td
(words)Tj
2.6702 0 Td
(may)Tj
-35.5065 -1.2983 Td
(avoid)Tj
2.4037 0 Td
(the)Tj
1.4627 0 Td
(set.)Tj
1.5193 0 Td
(Finding)Tj
3.3676 0 Td
(a)Tj
0.6463 0 Td
(minimum-size)Tj
6.1001 0 Td
(unavoidable)Tj
5.091 0 Td
(set)Tj
1.2982 0 Td
(for)Tj
1.3777 0 Td
(a)Tj
0.6519 0 Td
(given)Tj
/F10 1 Tf
2.3698 0 Td
[()]TJ
/F9 1 Tf
0.6803 0 Td
(can)Tj
1.6214 0 Td
(be)Tj
1.1452 0 Td
(solved)Tj
2.7326 0 Td
(in)Tj
1.0261 0 Td
(time)Tj
2.0239 0 Td
(poly-)Tj
-35.5178 -1.3039 Td
(nomial)Tj
3.0387 0 Td
(in)Tj
1.0374 0 Td
(the)Tj
1.4684 0 Td
(output)Tj
2.897 0 Td
(size)Tj
1.6837 0 Td
([)Tj
0.83 0.64 0.02 0 k
(16)Tj
0 g
(].)Tj
2.0807 0 Td
(The)Tj
1.7801 0 Td
(original)Tj
3.3279 0 Td
(algorithm)Tj
4.1555 0 Td
(is)Tj
0.8504 0 Td
(due)Tj
1.6951 0 Td
(to)Tj
1.0262 0 Td
(Mykkeltveit)Tj
4.9719 0 Td
([)Tj
0.83 0.64 0.02 0 k
(17)Tj
0 g
(].)Tj
2.0749 0 Td
(Its)Tj
1.2246 0 Td
(running)Tj
-33.3125 -1.2983 Td
(time)Tj
2.0295 0 Td
(is)Tj
/F10 1 Tf
0.8448 0 Td
[()]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[(#)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\)\),)Tj
4.3029 0 Td
(where)Tj
/F10 1 Tf
2.6532 0 Td
[(#)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
2.2337 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4684 0 Td
(size)Tj
1.6837 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4684 0 Td
(minimum)Tj
4.2916 0 Td
(unavoidable)Tj
5.0966 0 Td
(set.)Tj
/F10 1 Tf
1.5307 0 Td
[(#)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
2.2337 0 Td
(converges)Tj
4.2009 0 Td
(to)Tj
-35.9033 -1.2982 Td
(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 211.748 113.4425 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 215.2629 109.0204 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(/)Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
1.0147 0 Td
(\(an)Tj
1.5421 0 Td
(exact)Tj
2.262 0 Td
(formula)Tj
3.4129 0 Td
(is)Tj
0.8504 0 Td
(given)Tj
2.3811 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0318 0 Td
(Eq)Tj
1.2982 0 Td
(11)Tj
0 g
(\),)Tj
1.7348 0 Td
(so)Tj
1.0885 0 Td
(the)Tj
1.4684 0 Td
(running)Tj
3.4979 0 Td
(time)Tj
2.0296 0 Td
(is)Tj
/F10 1 Tf
0.8504 0 Td
[()]TJ
/F9 1 Tf
(\(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 482.0031 113.4425 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 485.4614 109.0204 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\).)Tj
-27.3484 -1.3039 Td
(An)Tj
1.457 0 Td
(unavoidable)Tj
5.0966 0 Td
(set)Tj
1.3039 0 Td
(of)Tj
1.0148 0 Td
(constant)Tj
3.6397 0 Td
(length)Tj
/F10 1 Tf
2.7269 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(is)Tj
0.8447 0 Td
(equivalent)Tj
4.354 0 Td
(to)Tj
1.0261 0 Td
(a)Tj
0.652 0 Td
(set)Tj
1.3039 0 Td
(of)Tj
1.0148 0 Td
(vertices)Tj
3.2427 0 Td
(in)Tj
1.0375 0 Td
(a)Tj
0.652 0 Td
(complete)Tj
3.8778 0 Td
(de)Tj
-35.1267 -1.2982 Td
(Bruijn)Tj
2.7723 0 Td
(graph)Tj
2.5342 0 Td
(of)Tj
1.0148 0 Td
(order)Tj
/F10 1 Tf
2.4207 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(whose)Tj
2.7213 0 Td
(removal)Tj
3.4752 0 Td
(turns)Tj
2.3301 0 Td
(it)Tj
0.7823 0 Td
(into)Tj
1.8425 0 Td
(a)Tj
0.652 0 Td
(directed)Tj
3.4866 0 Td
(acyclic)Tj
2.8913 0 Td
(graph)Tj
2.5341 0 Td
(\(DAG\).)Tj
3.2598 0 Td
(Each)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 169.285 23.6976 re
W* n
q
169.2283 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 450.4818 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Compact)Tj
4.1669 0 Td
(universal)Tj
/F7 1 Tf
4.1386 0 Td
(k)Tj
/F0 1 Tf
(-mer)Tj
2.7355 0 Td
(hitting)Tj
2.8346 0 Td
(sets)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
142.5827 34.9228 m
295.8236 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(Computationa)Tj
6.1229 0 Td
(l)Tj
0.4322 0 Td
(Biology)Tj
3.4371 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https:/)Tj
2.6788 0 Td
(/doi.org/10.13)Tj
6.0094 0 Td
(71/journal.p)Tj
5.1166 0 Td
(cbi.1005777)Tj
0 g
6.3497 0 Td
(October)Tj
3.7276 0 Td
(2,)Tj
1.0346 0 Td
(2017)Tj
26.901 0 Td
(4)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
84 0 obj
<>stream
endstream
endobj
85 0 obj
<>stream
endstream
endobj
86 0 obj
<>stream
endstream
endobj
87 0 obj
<>stream
endstream
endobj
88 0 obj
<>stream
endstream
endobj
89 0 obj
<>stream
endstream
endobj
90 0 obj
<>stream
endstream
endobj
91 0 obj
<>stream
BT
66.402 0 Td
(15)Tj
ET
Q
endstream
endobj
92 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 17 0 R/Annots 95 0 R/Contents 96 0 R/TrimBox[0 0 612 792]>>
endobj
95 0 obj
[97 0 R 98 0 R 99 0 R]
endobj
97 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.s002)>>
endobj
98 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref018)>>
endobj
99 0 obj
<>/Border[0 0 0]/A 100 0 R>>
endobj
100 0 obj
<>
endobj
96 0 obj
[101 0 R 102 0 R 103 0 R 104 0 R 105 0 R 106 0 R 107 0 R 108 0 R 109 0 R]
endobj
101 0 obj
<>stream
q
0.83 0.64 0.02 0 k
291.0614 541.3606 m
320.7685 541.3606 l
h
f*
545.6126 528.3213 m
555.137 528.3213 l
h
f*
0 g
1 j
1 J
0 w
10 0 0 10 200.0125 707.4141 cm
BT
/F10 1 Tf
1 TL
-0.004 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6475 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(set)Tj
1.3039 0 Td
(corresponds)Tj
5.1364 0 Td
(to)Tj
1.0261 0 Td
(a)Tj
0.6576 0 Td
(vertex,)Tj
2.88 0 Td
(and)Tj
1.7292 0 Td
(the)Tj
1.4683 0 Td
(removal)Tj
3.4809 0 Td
(of)Tj
1.0148 0 Td
(vertices)Tj
3.2428 0 Td
(from)Tj
2.2054 0 Td
(every)Tj
2.347 0 Td
(cycle)Tj
2.1884 0 Td
(guaran-)Tj
-33.8341 -1.3039 Td
(tees)Tj
1.7234 0 Td
(that)Tj
1.7801 0 Td
(no)Tj
1.2756 0 Td
(infinite)Tj
3.1295 0 Td
(sequence)Tj
3.8551 0 Td
(is)Tj
0.8503 0 Td
(represented)Tj
4.9096 0 Td
(as)Tj
1.0148 0 Td
(a)Tj
0.652 0 Td
(path)Tj
2.0012 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.4684 0 Td
(graph.)Tj
2.7609 0 Td
(This)Tj
1.9899 0 Td
(set)Tj
1.3039 0 Td
(is)Tj
0.8448 0 Td
(known)Tj
3.0047 0 Td
(as)Tj
1.0148 0 Td
(a)Tj
/F10 1 Tf
0.6576 0 Td
[()4()7( )-9($%)]TJ
-35.2684 -1.2982 Td
[( )13()12()12()13()]TJ
2.0352 0 Td
[(\n)-3()8()]TJ
/F9 1 Tf
(.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 650.4377 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(Hitting)Tj
3.0141 0 Td
(remaining)Tj
4.5544 0 Td
(length)Tj
/F7 1 Tf
2.9055 0 Td
(L)Tj
/F0 1 Tf
0.7654 0 Td
(sequences)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 633.4299 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(Unfortunately,)Tj
6.1284 0 Td
(finding)Tj
3.1294 0 Td
(an)Tj
1.2019 0 Td
(unavoidable)Tj
5.0967 0 Td
(set)Tj
1.3039 0 Td
(is)Tj
0.8504 0 Td
(not)Tj
1.5704 0 Td
(enough,)Tj
3.4469 0 Td
(as)Tj
1.0148 0 Td
(there)Tj
2.2677 0 Td
(may)Tj
1.9275 0 Td
(be)Tj
/F10 1 Tf
1.1509 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.863 0 Td
(sequences)Tj
-31.9519 -1.2982 Td
(that)Tj
1.7744 0 Td
(avoid)Tj
2.4151 0 Td
(that)Tj
1.7745 0 Td
(set.)Tj
1.5307 0 Td
(Thus,)Tj
2.4718 0 Td
(we)Tj
1.3266 0 Td
(need)Tj
2.143 0 Td
(additional)Tj
/F10 1 Tf
4.2803 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0103 0 Td
(to)Tj
1.0262 0 Td
(hit)Tj
1.3096 0 Td
(those.)Tj
2.5682 0 Td
(If)Tj
0.8447 0 Td
(we)Tj
1.3266 0 Td
(consider)Tj
3.651 0 Td
(the)Tj
1.4683 0 Td
(graph)Tj
2.5398 0 Td
(for-)Tj
-35.4611 -1.3039 Td
(mulation,)Tj
4.0932 0 Td
(after)Tj
2.0352 0 Td
(removal)Tj
3.4753 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
0.6519 0 Td
(decycling)Tj
4.0025 0 Td
(set)Tj
1.304 0 Td
(from)Tj
2.2053 0 Td
(the)Tj
1.4683 0 Td
(graph)Tj
2.5342 0 Td
(we)Tj
1.3323 0 Td
(are)Tj
1.4456 0 Td
(left)Tj
1.474 0 Td
(with)Tj
2.0013 0 Td
(a)Tj
0.6519 0 Td
(DAG,)Tj
2.5796 0 Td
(which)Tj
2.6532 0 Td
(may)Tj
-34.9226 -1.2983 Td
(contain)Tj
3.2428 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F17 1 Tf
1.0885 0 Td
[()]TJ
/F10 1 Tf
0.788 0 Td
[()]TJ
/F9 1 Tf
(\)-long)Tj
3.1408 0 Td
(paths)Tj
2.3584 0 Td
(representing)Tj
/F10 1 Tf
5.2384 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.8629 0 Td
(sequences.)Tj
4.4391 0 Td
(We)Tj
1.61 0 Td
(need)Tj
2.143 0 Td
(to)Tj
1.0205 0 Td
(remove)Tj
3.2201 0 Td
(additional)Tj
4.2746 0 Td
(verti-)Tj
-35.4271 -1.2983 Td
(ces,)Tj
1.6497 0 Td
(so)Tj
1.0885 0 Td
(that)Tj
1.7801 0 Td
(there)Tj
2.2621 0 Td
(is)Tj
0.8504 0 Td
(no)Tj
1.2756 0 Td
(path)Tj
1.9955 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F17 1 Tf
2.7326 0 Td
[()]TJ
/F9 1 Tf
0.6236 0 Td
(=)Tj
/F10 1 Tf
0.7994 0 Td
[()]TJ
/F17 1 Tf
0.7483 0 Td
[()]TJ
/F10 1 Tf
0.7881 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.907 0 Td
(The)Tj
1.7859 0 Td
(problem)Tj
3.6113 0 Td
(of)Tj
1.0148 0 Td
(finding)Tj
3.1294 0 Td
(a)Tj
0.6576 0 Td
(minimum-size)Tj
6.1058 0 Td
(set)Tj
1.2983 0 Td
(of)Tj
-36.1188 -1.3039 Td
(vertices)Tj
3.2428 0 Td
(that)Tj
1.7801 0 Td
(hit)Tj
1.3096 0 Td
(all)Tj
/F17 1 Tf
1.1452 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.7439 0 Td
(paths)Tj
2.3584 0 Td
(in)Tj
1.0318 0 Td
(a)Tj
0.6577 0 Td
(general)Tj
3.1294 0 Td
(directed)Tj
3.4866 0 Td
(acyclic)Tj
2.8913 0 Td
(graph)Tj
2.5342 0 Td
(is)Tj
0.8504 0 Td
(known)Tj
3.0047 0 Td
(to)Tj
1.0204 0 Td
(be)Tj
1.1509 0 Td
(NP-hard,)Tj
3.9515 0 Td
(as)Tj
-36.2889 -1.2982 Td
(we)Tj
1.3266 0 Td
(review)Tj
2.8459 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.474 0 Td
(Appendix)Tj
4.1669 0 Td
(\(see)Tj
1.7688 0 Td
(Appendix,)Tj
4.3994 0 Td
(Subsection)Tj
4.5581 0 Td
(NP-hardness)Tj
5.4198 0 Td
(of)Tj
1.0148 0 Td
(MINIMUM)Tj
/F17 1 Tf
5.0513 0 Td
[()]TJ
/F9 1 Tf
(-PATH)Tj
-33.0574 -1.2983 Td
(COVER)Tj
3.5149 0 Td
(IN)Tj
1.2982 0 Td
(A)Tj
0.9015 0 Td
(DAG)Tj
2.3584 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0318 0 Td
(S1)Tj
1.1735 0 Td
(Text)Tj
0 g
(\).)Tj
2.5852 0 Td
(Therefore,)Tj
4.388 0 Td
(we)Tj
1.3323 0 Td
(give)Tj
1.8255 0 Td
(a)Tj
0.6576 0 Td
(heuristic)Tj
3.685 0 Td
(solution.)Tj
-23.5557 -1.3039 Td
(Our)Tj
1.8708 0 Td
(initial)Tj
2.5455 0 Td
(algorithm)Tj
4.1556 0 Td
(is)Tj
0.8504 0 Td
(based)Tj
2.4718 0 Td
(on)Tj
1.2755 0 Td
(the)Tj
1.4684 0 Td
(greedy)Tj
2.8856 0 Td
(algorithm)Tj
4.1556 0 Td
(for)Tj
1.389 0 Td
(the)Tj
1.4683 0 Td
(minimum)Tj
4.2916 0 Td
(hitting)Tj
2.8913 0 Td
(set)Tj
1.304 0 Td
([)Tj
0.83 0.64 0.02 0 k
(18)Tj
0 g
(].)Tj
-34.2196 -1.2983 Td
(We)Tj
1.61 0 Td
(define)Tj
2.6986 0 Td
(the)Tj
/F10 1 Tf
1.4683 0 Td
[()18()14()7()12()13()]TJ
2.795 0 Td
[()18(\r)12()17()4()2()]TJ
3.2825 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.8141 0 Td
[(')]TJ
/F9 1 Tf
(\))Tj
0.9525 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
0.6519 0 Td
(vertex)Tj
/F10 1 Tf
2.6589 0 Td
[()]TJ
/F9 1 Tf
0.652 0 Td
(to)Tj
1.0261 0 Td
(be)Tj
1.1509 0 Td
(the)Tj
1.4683 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
1.0148 0 Td
(paths)Tj
2.3584 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7269 0 Td
[(')]TJ
/F9 1 Tf
0.6123 0 Td
(that)Tj
-34.3897 -1.2983 Td
(contain)Tj
/F10 1 Tf
3.2484 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.8788 0 Td
(The)Tj
1.7801 0 Td
(main)Tj
2.2904 0 Td
(observation)Tj
4.8982 0 Td
(is)Tj
0.8504 0 Td
(that)Tj
1.7745 0 Td
(we)Tj
1.3266 0 Td
(can)Tj
1.6271 0 Td
(calculate)Tj
3.6793 0 Td
(the)Tj
1.4684 0 Td
(hitting)Tj
2.8913 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(each)Tj
2.0296 0 Td
(vertex)Tj
2.6589 0 Td
(effi-)Tj
-35.8353 -1.2982 Td
(ciently)Tj
2.8799 0 Td
(using)Tj
2.3925 0 Td
(dynamic)Tj
3.6906 0 Td
(programming.)Tj
6.0321 0 Td
(The)Tj
1.7858 0 Td
(solution)Tj
3.481 0 Td
(is)Tj
0.8504 0 Td
(based)Tj
2.4718 0 Td
(on)Tj
1.2755 0 Td
(calculating)Tj
4.5354 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(paths)Tj
-35.2967 -1.3039 Td
(of)Tj
1.0147 0 Td
(length)Tj
/F10 1 Tf
2.727 0 Td
[()]TJ
/F9 1 Tf
0.4875 0 Td
(that)Tj
1.7802 0 Td
(terminate)Tj
4.1045 0 Td
(at)Tj
0.9524 0 Td
(vertex)Tj
/F10 1 Tf
2.6532 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.8845 0 Td
(and)Tj
1.7291 0 Td
(the)Tj
1.4683 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
1.0148 0 Td
(paths)Tj
2.3584 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7269 0 Td
[()]TJ
/F9 1 Tf
0.4875 0 Td
(that)Tj
1.7802 0 Td
(start)Tj
1.9842 0 Td
(at)Tj
0.9525 0 Td
(vertex)Tj
/F10 1 Tf
2.6532 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
-36.1925 -1.2983 Td
(for)Tj
1.3832 0 Td
(all)Tj
/F10 1 Tf
1.1509 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.652 0 Td
(2)Tj
/F10 1 Tf
-0.004 Tc
0.8787 0 Td
[(\()]TJ
/F9 1 Tf
0.8787 0 Td
(and)Tj
1.7348 0 Td
(0)Tj
/F15 1 Tf
0 Tc
0.6917 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.4876 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[(')]TJ
/F9 1 Tf
(.)Tj
0.839 0 Td
(Then,)Tj
2.5569 0 Td
(the)Tj
1.4683 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[(')]TJ
/F9 1 Tf
(-long)Tj
2.7269 0 Td
(paths)Tj
2.3584 0 Td
(through)Tj
/F10 1 Tf
3.4469 0 Td
[()]TJ
/F9 1 Tf
0.652 0 Td
(is)Tj
0.8503 0 Td
(directly)Tj
3.2315 0 Td
(computable)Tj
-32.4054 -1.2983 Td
(from)Tj
2.2053 0 Td
(these)Tj
2.2507 0 Td
(values)Tj
2.6702 0 Td
(by)Tj
1.1792 0 Td
(breaking)Tj
3.736 0 Td
(any)Tj
1.6555 0 Td
(path)Tj
1.9955 0 Td
(into)Tj
1.8426 0 Td
(an)Tj
/F10 1 Tf
1.2018 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.6079 0 Td
(path)Tj
1.9956 0 Td
(ending)Tj
2.999 0 Td
(at)Tj
/F10 1 Tf
0.9524 0 Td
[()]TJ
/F9 1 Tf
0.6577 0 Td
(and)Tj
1.7291 0 Td
(an)Tj
1.2019 0 Td
(\()Tj
/F10 1 Tf
[(')]TJ
/F17 1 Tf
0.9524 0 Td
[()]TJ
/F10 1 Tf
0.788 0 Td
[()]TJ
/F9 1 Tf
(\)-long)Tj
2.9481 0 Td
(path)Tj
-35.5689 -1.3039 Td
(starting)Tj
3.2598 0 Td
(at)Tj
/F10 1 Tf
0.9524 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.8844 0 Td
(for)Tj
1.3833 0 Td
(all)Tj
1.1452 0 Td
(possible)Tj
3.4129 0 Td
(values)Tj
2.6645 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.7144 0 Td
(We)Tj
1.61 0 Td
(set)Tj
/F10 1 Tf
1.304 0 Td
[(')]TJ
/F9 1 Tf
0.6066 0 Td
(=)Tj
/F10 1 Tf
0.805 0 Td
[()]TJ
/F17 1 Tf
0.7427 0 Td
[()]TJ
/F10 1 Tf
0.7937 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(to)Tj
1.0204 0 Td
(get)Tj
1.4117 0 Td
(the)Tj
1.4683 0 Td
(desired)Tj
3.1238 0 Td
(hitting)Tj
2.8913 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
-35.3137 -1.2982 Td
(each)Tj
2.0295 0 Td
(vertex.)Tj
-0.8333 -1.2983 Td
(Specifically,)Tj
4.9152 0 Td
(let)Tj
/F10 1 Tf
1.1849 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 279.7228 416.0692 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 284.3149 412.4409 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(=)Tj
0.7993 0 Td
(\()Tj
/F10 1 Tf
[(\()]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 302.3433 416.0692 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 304.7811 412.4409 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
/F10 1 Tf
0.4422 0 Td
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 314.7023 416.0692 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 317.0834 412.4409 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\))Tj
0.5612 0 Td
(be)Tj
1.1509 0 Td
(the)Tj
1.4683 0 Td
(directed)Tj
3.4866 0 Td
(acyclic)Tj
2.8913 0 Td
(graph,)Tj
2.7609 0 Td
(after)Tj
2.0353 0 Td
(removal)Tj
3.4753 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(decycling)Tj
4.0025 0 Td
(set.)Tj
-36.0224 -1.3039 Td
(Denote)Tj
3.1578 0 Td
(by)Tj
/F10 1 Tf
1.1792 0 Td
[()]TJ
/F9 1 Tf
0.9128 0 Td
(and)Tj
/F10 1 Tf
1.7348 0 Td
[(*)]TJ
/F9 1 Tf
0.737 0 Td
(matrices)Tj
3.6169 0 Td
(of)Tj
1.0147 0 Td
(size)Tj
1.6838 0 Td
(|)Tj
/F10 1 Tf
[(\()]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 349.5685 403.0299 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 352.0062 399.4015 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(|)Tj
/F17 1 Tf
0.4762 0 Td
[()]TJ
/F9 1 Tf
0.788 0 Td
(\()Tj
/F10 1 Tf
[(')]TJ
/F9 1 Tf
0.9524 0 Td
(+)Tj
0.7994 0 Td
(1\))Tj
1.0375 0 Td
(where)Tj
/F10 1 Tf
2.6475 0 Td
[()]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.9162 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
0.8277 0 Td
(is)Tj
0.8447 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.6079 0 Td
(paths)Tj
2.3584 0 Td
(in)Tj
/F10 1 Tf
-36.3568 -1.2982 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 206.759 390.0472 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 211.3511 386.4188 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(starting)Tj
3.2598 0 Td
(at)Tj
0.9524 0 Td
(vertex)Tj
/F10 1 Tf
2.6589 0 Td
[()]TJ
/F9 1 Tf
0.652 0 Td
(and)Tj
/F10 1 Tf
1.7347 0 Td
[(*)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.7348 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
0.8277 0 Td
(is)Tj
0.8448 0 Td
(the)Tj
1.474 0 Td
(number)Tj
3.4129 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.6078 0 Td
(paths)Tj
2.3584 0 Td
(ending)Tj
2.9991 0 Td
(at)Tj
0.9524 0 Td
(vertex)Tj
/F10 1 Tf
2.6589 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
-30.0811 -1.2982 Td
(The)Tj
1.7858 0 Td
(calculation)Tj
4.5751 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
0.9128 0 Td
(and)Tj
/F10 1 Tf
1.7348 0 Td
[(*)]TJ
/F9 1 Tf
0.737 0 Td
(is)Tj
0.8447 0 Td
(done)Tj
2.228 0 Td
(recursively)Tj
4.5467 0 Td
(as)Tj
1.0148 0 Td
(follows:)Tj
/F10 1 Tf
0 Tc
-9.7681 -1.8539 Td
[()]TJ
/F15 1 Tf
()Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
1.542 0 Td
(;)Tj
/F18 1 Tf
0.4366 0 Td
(0)Tj
/F15 1 Tf
()Tj
1.1622 0 Td
()Tj
/F10 1 Tf
1.0488 0 Td
[(*)]TJ
/F15 1 Tf
0.5726 0 Td
()Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
0.8447 0 Td
(;)Tj
/F18 1 Tf
0.4365 0 Td
(0)Tj
/F15 1 Tf
()Tj
1.1622 0 Td
()Tj
/F18 1 Tf
1.0488 0 Td
(1)Tj
/F20 1 Tf
(;)Tj
/F17 1 Tf
0.9355 0 Td
[()8()11()]TJ
1.5477 0 Td
[()-4( )-5( )]TJ
/F10 1 Tf
1.3323 0 Td
[()]TJ
/F15 1 Tf
0.7313 0 Td
(2)Tj
/F10 1 Tf
0.9354 0 Td
[(\()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 453.0897 359.0362 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 563.4708 354.8976 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F9 1 Tf
(1)Tj
/F15 1 Tf
()Tj
/F10 1 Tf
-23.516 -2.8969 Td
[()]TJ
/F15 1 Tf
()Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
1.542 0 Td
(;)Tj
/F10 1 Tf
0.4365 0 Td
[()]TJ
/F15 1 Tf
()Tj
0.9298 0 Td
()Tj
/F21 1 Tf
1.4003 0.9524 Td
(X)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 367.8803 315.3259 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
(;)Tj
/F10 1 Tf
1.1149 0 Td
[(\r)]TJ
/F15 1 Tf
(2)Tj
/F10 1 Tf
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 387.3826 317.0267 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 390.9543 325.9275 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F15 1 Tf
()Tj
/F10 1 Tf
[(\r)]TJ
/F20 1 Tf
(;)Tj
/F10 1 Tf
2.0522 0 Td
[()]TJ
/F15 1 Tf
0.4932 0 Td
( )Tj
/F18 1 Tf
0.9922 0 Td
(1)Tj
/F15 1 Tf
()Tj
13.7139 0 Td
()Tj
/F9 1 Tf
(2)Tj
/F15 1 Tf
()Tj
/F10 1 Tf
-23.3913 -3.9571 Td
[(*)]TJ
/F15 1 Tf
0.5726 0 Td
()Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
0.8448 0 Td
(;)Tj
/F10 1 Tf
0.4365 0 Td
[()]TJ
/F15 1 Tf
()Tj
0.9298 0 Td
()Tj
/F21 1 Tf
1.4003 0.9468 Td
(X)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 367.8803 275.6976 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F10 1 Tf
[(\r)]TJ
/F20 1 Tf
(;)Tj
/F10 1 Tf
[()]TJ
/F15 1 Tf
1.6441 0 Td
(2)Tj
/F10 1 Tf
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 387.3826 277.4551 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 390.9543 286.3559 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[(*)]TJ
/F15 1 Tf
0.5669 0 Td
()Tj
/F10 1 Tf
[(\r)]TJ
/F20 1 Tf
(;)Tj
/F10 1 Tf
1.3606 0 Td
[()]TJ
/F15 1 Tf
0.4932 0 Td
( )Tj
/F18 1 Tf
0.9921 0 Td
(1)Tj
/F15 1 Tf
()Tj
13.8387 0 Td
()Tj
/F9 1 Tf
(3)Tj
/F15 1 Tf
()Tj
/F9 1 Tf
-0.004 Tc
-36.3455 -3.2144 Td
(To)Tj
1.3379 0 Td
(get)Tj
1.406 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[(')]TJ
/F9 1 Tf
(-long)Tj
2.7326 0 Td
(paths)Tj
2.3584 0 Td
(that)Tj
1.7745 0 Td
(vertex)Tj
/F10 1 Tf
2.6589 0 Td
[()]TJ
/F9 1 Tf
0.6519 0 Td
(participates)Tj
4.8358 0 Td
(in,)Tj
1.2586 0 Td
(we)Tj
1.3266 0 Td
(sum:)Tj
/F10 1 Tf
0 Tc
-14.6379 -2.7666 Td
[(&)]TJ
/F15 1 Tf
0.6633 0 Td
()Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
0.8447 0 Td
(;)Tj
0.4365 0 Td
(`)Tj
/F15 1 Tf
()Tj
1.0658 0 Td
()Tj
/F21 1 Tf
1.0489 0.9468 Td
(X)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 362.6078 238.0535 cm
BT
/F20 1 Tf
1 TL
0 0 Td
(`)Tj
/F10 1 Tf
-0.5669 -3.6568 Td
[()]TJ
/F15 1 Tf
()Tj
/F18 1 Tf
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 372.6425 226.5448 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[(*)]TJ
/F15 1 Tf
0.5725 0 Td
()Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
0.8448 0 Td
(;)Tj
/F10 1 Tf
0.4365 0 Td
[()]TJ
/F15 1 Tf
()Tj
0.8787 0 Td
()Tj
/F10 1 Tf
0.4933 0 Td
[()]TJ
/F15 1 Tf
()Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
1.542 0 Td
(;)Tj
0.4309 0 Td
(`)Tj
/F15 1 Tf
0.6292 0 Td
( )Tj
/F10 1 Tf
0.9922 0 Td
[()]TJ
/F15 1 Tf
()Tj
12.2626 0 Td
()Tj
/F9 1 Tf
(4)Tj
/F15 1 Tf
()Tj
/F9 1 Tf
-0.004 Tc
-36.3455 -3.0557 Td
(The)Tj
1.7688 0 Td
(running)Tj
3.4866 0 Td
(time)Tj
2.0182 0 Td
(is)Tj
0.8391 0 Td
(proportional)Tj
5.3064 0 Td
(to)Tj
1.0148 0 Td
(the)Tj
1.457 0 Td
(sum)Tj
1.9161 0 Td
(of)Tj
1.0091 0 Td
(all)Tj
1.1339 0 Td
(vertex)Tj
2.6475 0 Td
(degrees)Tj
3.2031 0 Td
(\(which)Tj
2.9821 0 Td
(is)Tj
/F22 1 Tf
0.839 0 Td
( )Tj
/F9 1 Tf
(\(|)Tj
/F10 1 Tf
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 514.9417 199.6157 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 517.0393 195.9874 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(|\)\))Tj
1.1451 0 Td
(times)Tj
/F10 1 Tf
2.3811 0 Td
[(')]TJ
/F9 1 Tf
(,)Tj
0.8277 0 Td
(giv-)Tj
-36.0563 -1.3039 Td
(ing)Tj
1.5023 0 Td
(a)Tj
0.652 0 Td
(running)Tj
3.4979 0 Td
(time)Tj
2.0296 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(\(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 309.0897 187.4267 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 322.6393 182.948 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.4932 0 Td
[(')]TJ
/F9 1 Tf
(\))Tj
0.9524 0 Td
(for)Tj
/F10 1 Tf
1.3833 0 Td
[(')]TJ
/F9 1 Tf
0.6123 0 Td
(=)Tj
/F10 1 Tf
0.7994 0 Td
[()]TJ
/F17 1 Tf
0.7483 0 Td
[()]TJ
/F10 1 Tf
0.788 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 151.9937 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(The)Tj
1.9275 0 Td
(DOCKS)Tj
3.7512 0 Td
(algorithm)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 134.9858 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(The)Tj
1.7801 0 Td
(full)Tj
1.5307 0 Td
(algorithm)Tj
4.1556 0 Td
(combines)Tj
4.0762 0 Td
(the)Tj
1.4683 0 Td
(two)Tj
1.7121 0 Td
(steps.)Tj
2.4038 0 Td
(First,)Tj
2.2733 0 Td
(we)Tj
1.3266 0 Td
(find)Tj
1.8539 0 Td
(a)Tj
0.652 0 Td
(decycling)Tj
3.9968 0 Td
(set)Tj
1.3039 0 Td
(in)Tj
1.0375 0 Td
(a)Tj
0.652 0 Td
(complete)Tj
3.8834 0 Td
(de)Tj
-34.1062 -1.2982 Td
(Bruijn)Tj
2.7722 0 Td
(graph)Tj
2.5342 0 Td
(of)Tj
1.0148 0 Td
(order)Tj
/F10 1 Tf
2.4207 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(and)Tj
1.7291 0 Td
(remove)Tj
3.2202 0 Td
(it)Tj
0.7823 0 Td
(from)Tj
2.211 0 Td
(the)Tj
1.4684 0 Td
(graph,)Tj
2.7609 0 Td
(obtaining)Tj
4.0592 0 Td
(a)Tj
0.6576 0 Td
(DAG.)Tj
2.5795 0 Td
(Then,)Tj
2.5569 0 Td
(we)Tj
1.3266 0 Td
(repeatedly)Tj
-32.7796 -1.2983 Td
(remove)Tj
3.2201 0 Td
(a)Tj
0.652 0 Td
(vertex)Tj
/F10 1 Tf
2.6588 0 Td
[()]TJ
/F9 1 Tf
0.652 0 Td
(with)Tj
1.9956 0 Td
(the)Tj
1.474 0 Td
(largest)Tj
2.8176 0 Td
(hitting)Tj
2.8913 0 Td
(number)Tj
/F10 1 Tf
3.4186 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.8085 0 Td
[(')]TJ
/F9 1 Tf
(\))Tj
0.9524 0 Td
(until)Tj
2.109 0 Td
(there)Tj
2.262 0 Td
(are)Tj
1.4513 0 Td
(no)Tj
/F10 1 Tf
1.2756 0 Td
[(')]TJ
/F9 1 Tf
(-long)Tj
2.7269 0 Td
(paths,)Tj
-32.3657 -1.3039 Td
(recomputing)Tj
/F10 1 Tf
5.3857 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[(\r)]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.9049 0 Td
[(')]TJ
/F9 1 Tf
(\))Tj
0.9524 0 Td
(for)Tj
1.389 0 Td
(all)Tj
1.1452 0 Td
(remaining)Tj
4.3653 0 Td
(vertices)Tj
/F10 1 Tf
3.2428 0 Td
[(\r)]TJ
/F9 1 Tf
0.7484 0 Td
(after)Tj
2.0353 0 Td
(each)Tj
2.0295 0 Td
(removal.)Tj
3.6964 0 Td
(This)Tj
1.9899 0 Td
(is)Tj
0.8504 0 Td
(summarized)Tj
5.1817 0 Td
(below)Tj
-34.9169 -1.2983 Td
(\(Algorithm)Tj
4.7451 0 Td
(1\).)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 169.285 23.6976 re
W* n
q
169.2283 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 450.4818 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Compact)Tj
4.1669 0 Td
(universal)Tj
/F7 1 Tf
4.1386 0 Td
(k)Tj
/F0 1 Tf
(-mer)Tj
2.7355 0 Td
(hitting)Tj
2.8346 0 Td
(sets)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
142.5827 34.9228 m
295.8236 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(Computationa)Tj
6.1229 0 Td
(l)Tj
0.4322 0 Td
(Biology)Tj
3.4371 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https:/)Tj
2.6788 0 Td
(/doi.org/10.13)Tj
6.0094 0 Td
(71/journal.p)Tj
5.1166 0 Td
(cbi.1005777)Tj
0 g
6.3497 0 Td
(October)Tj
3.7276 0 Td
(2,)Tj
1.0346 0 Td
(2017)Tj
26.901 0 Td
(5)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
102 0 obj
<>stream
endstream
endobj
103 0 obj
<>stream
endstream
endobj
104 0 obj
<>stream
endstream
endobj
105 0 obj
<>stream
endstream
endobj
106 0 obj
<>stream
endstream
endobj
107 0 obj
<>stream
endstream
endobj
108 0 obj
<>stream
endstream
endobj
109 0 obj
<>stream
BT
66.402 0 Td
(15)Tj
ET
Q
endstream
endobj
110 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 17 0 R/Annots 111 0 R/Contents 112 0 R/TrimBox[0 0 612 792]>>
endobj
111 0 obj
[113 0 R 114 0 R]
endobj
113 0 obj
<>/Border[0 0 0]/Dest(Rsec012)>>
endobj
114 0 obj
<>/Border[0 0 0]/A 115 0 R>>
endobj
115 0 obj
<>
endobj
112 0 obj
[116 0 R 117 0 R 118 0 R 119 0 R 120 0 R 121 0 R 122 0 R]
endobj
116 0 obj
<>stream
q
0.83 0.64 0.02 0 k
217.7008 450.1417 m
246.0472 450.1417 l
h
f*
0 g
1 j
1 J
0 w
10 0 0 10 211.9748 516.2456 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(Finding)Tj
3.3732 0 Td
(the)Tj
1.4683 0 Td
(decycling)Tj
4.0025 0 Td
(set)Tj
1.3039 0 Td
(takes)Tj
/F10 1 Tf
2.2337 0 Td
[()]TJ
/F9 1 Tf
(\(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 357.9023 520.6677 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 361.3606 516.2456 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\).)Tj
0.788 0 Td
(In)Tj
1.1055 0 Td
(the)Tj
1.474 0 Td
(second)Tj
3.0104 0 Td
(phase,)Tj
2.7042 0 Td
(each)Tj
2.0296 0 Td
(iteration)Tj
3.634 0 Td
(calculates)Tj
4.0422 0 Td
(the)Tj
-34.9226 -1.3039 Td
(hitting)Tj
2.8914 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(all)Tj
1.1452 0 Td
(vertices)Tj
3.2428 0 Td
(in)Tj
1.0375 0 Td
(time)Tj
/F10 1 Tf
2.0296 0 Td
[()]TJ
/F9 1 Tf
(\(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 369.9212 507.685 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 381.2598 503.2062 cm
BT
/F10 1 Tf
1 TL
-0.004 Tc
0 0 Td
[(')]TJ
/F9 1 Tf
(\).)Tj
1.1792 0 Td
(The)Tj
1.7801 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
1.0148 0 Td
(iterations)Tj
3.9968 0 Td
(is)Tj
0.8504 0 Td
(1)Tj
0.6916 0 Td
(+)Tj
/F10 1 Tf
0.8051 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9184 0 Td
(where)Tj
/F10 1 Tf
2.6475 0 Td
[()]TJ
/F9 1 Tf
0.6973 0 Td
(is)Tj
-36.1244 -1.2982 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(vertices)Tj
3.2428 0 Td
(removed.)Tj
3.9742 0 Td
(Thus,)Tj
2.4718 0 Td
(the)Tj
1.4683 0 Td
(total)Tj
2.0068 0 Td
(running)Tj
3.4923 0 Td
(time)Tj
2.0296 0 Td
(is)Tj
0.8504 0 Td
(dominated)Tj
4.5751 0 Td
(by)Tj
1.1792 0 Td
(steps)Tj
2.1826 0 Td
(48)Tj
1.6895 0 Td
(and)Tj
1.7291 0 Td
(is)Tj
/F10 1 Tf
-36.7934 -1.2983 Td
[()]TJ
/F9 1 Tf
(\(\(1)Tj
2.0693 0 Td
(+)Tj
/F10 1 Tf
0.7994 0 Td
[()]TJ
/F9 1 Tf
(\)|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 248.5984 481.6629 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 259.9937 477.2409 cm
BT
/F10 1 Tf
1 TL
-0.004 Tc
0 0 Td
[(')]TJ
/F9 1 Tf
(\).)Tj
-4.8018 -1.3039 Td
(The)Tj
1.7801 0 Td
(exponential)Tj
4.8982 0 Td
(dependence)Tj
5.0003 0 Td
(of)Tj
1.0148 0 Td
(DOCKS)Tj
3.5092 0 Td
(on)Tj
/F10 1 Tf
1.2699 0 Td
[()]TJ
/F9 1 Tf
0.6803 0 Td
(limits)Tj
2.4775 0 Td
(the)Tj
1.4683 0 Td
(range)Tj
2.4548 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
0.6803 0 Td
(to)Tj
1.0205 0 Td
(which)Tj
2.6476 0 Td
(it)Tj
0.7823 0 Td
(can)Tj
1.6214 0 Td
(be)Tj
1.1452 0 Td
(applied)Tj
-34.6617 -1.2982 Td
(\(see)Tj
0.83 0.64 0.02 0 k
1.7688 0 Td
(Results)Tj
0 g
(,)Tj
3.2825 0 Td
(Subsection)Tj
4.558 0 Td
(DOCKS\).)Tj
4.0818 0 Td
(This)Tj
1.9899 0 Td
(motivates)Tj
4.0819 0 Td
(us)Tj
1.1055 0 Td
(to)Tj
1.0261 0 Td
(develop)Tj
3.3222 0 Td
(two)Tj
1.7065 0 Td
(variants)Tj
3.3902 0 Td
(that)Tj
1.7801 0 Td
(trade)Tj
2.2734 0 Td
(larger)Tj
-34.3669 -1.2983 Td
(solution)Tj
3.4809 0 Td
(sizes)Tj
2.0466 0 Td
(for)Tj
1.3832 0 Td
(faster)Tj
2.3981 0 Td
(running)Tj
3.4979 0 Td
(times)Tj
2.3868 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(different)Tj
3.6567 0 Td
(heuristics)Tj
4.0478 0 Td
(described)Tj
4.0535 0 Td
(next.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 402.1795 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(The)Tj
1.9275 0 Td
(DOCKSany)Tj
5.3434 0 Td
(algorithms)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 385.2283 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(In)Tj
1.1055 0 Td
(order)Tj
2.4207 0 Td
(to)Tj
1.0262 0 Td
(extend)Tj
2.9083 0 Td
(the)Tj
1.4683 0 Td
(range)Tj
2.4662 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
0.907 0 Td
[()]TJ
/F9 1 Tf
0.7484 0 Td
(values)Tj
2.6702 0 Td
(beyond)Tj
3.1861 0 Td
(what)Tj
2.1657 0 Td
(DOCKS)Tj
3.5149 0 Td
(can)Tj
1.6271 0 Td
(compute)Tj
3.736 0 Td
(in)Tj
1.0318 0 Td
(reasonable)Tj
-31.9972 -1.3039 Td
(times,)Tj
2.6135 0 Td
(we)Tj
1.3266 0 Td
(develop)Tj
3.3222 0 Td
(a)Tj
0.6519 0 Td
(faster)Tj
2.3981 0 Td
(heuristic)Tj
3.685 0 Td
(that)Tj
1.7802 0 Td
(may)Tj
1.9275 0 Td
(produce)Tj
3.5206 0 Td
(cruder)Tj
2.863 0 Td
(solutions.)Tj
4.0705 0 Td
(Instead)Tj
3.1521 0 Td
(of)Tj
1.0148 0 Td
(calculating)Tj
-32.326 -1.2982 Td
(the)Tj
1.4683 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[(')]TJ
/F9 1 Tf
(-long)Tj
2.727 0 Td
(paths)Tj
2.3584 0 Td
(through)Tj
3.4469 0 Td
(each)Tj
2.0296 0 Td
(vertex,)Tj
2.88 0 Td
(we)Tj
1.3266 0 Td
(consider)Tj
/F10 1 Tf
3.651 0 Td
[()11()4()]TJ
/F9 1 Tf
1.1792 0 Td
(paths)Tj
2.3584 0 Td
(through)Tj
3.4469 0 Td
(each)Tj
2.0239 0 Td
(vertex.)Tj
-33.3295 -1.2983 Td
(This)Tj
1.9842 0 Td
(number,)Tj
3.6453 0 Td
(denoted)Tj
3.4753 0 Td
(by)Tj
/F10 1 Tf
1.1792 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\),)Tj
2.1543 0 Td
(can)Tj
1.6271 0 Td
(be)Tj
1.1452 0 Td
(calculated)Tj
4.2066 0 Td
(more)Tj
2.3414 0 Td
(quickly)Tj
3.1407 0 Td
(and)Tj
1.7348 0 Td
(serve)Tj
2.2507 0 Td
(as)Tj
1.0148 0 Td
(an)Tj
1.2019 0 Td
(estimate)Tj
3.5489 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
-35.6652 -1.3039 Td
[(')]TJ
/F9 1 Tf
(\).)Tj
1.1792 0 Td
(We)Tj
1.6044 0 Td
(call)Tj
1.5703 0 Td
(this)Tj
1.6781 0 Td
(heuristic)Tj
3.6851 0 Td
(DOCKSany)Tj
4.9549 0 Td
(\(Algorithm)Tj
4.7452 0 Td
(2\).)Tj
-18.221 -1.2983 Td
(DOCKSany)Tj
4.9549 0 Td
(has)Tj
1.542 0 Td
(the)Tj
1.4684 0 Td
(same)Tj
2.262 0 Td
(structure)Tj
3.8211 0 Td
(as)Tj
1.0148 0 Td
(DOCKS,)Tj
3.7417 0 Td
(but)Tj
1.5534 0 Td
(with)Tj
1.9955 0 Td
(one)Tj
1.7008 0 Td
(difference:)Tj
4.4277 0 Td
(it)Tj
0.788 0 Td
(removes)Tj
3.5773 0 Td
(a)Tj
0.6577 0 Td
(node)Tj
/F10 1 Tf
2.2223 0 Td
[()]TJ
/F9 1 Tf
-36.9238 -1.2982 Td
(with)Tj
1.9955 0 Td
(maximum)Tj
/F10 1 Tf
4.371 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
1.9276 0 Td
(in)Tj
1.0374 0 Td
(each)Tj
2.024 0 Td
(iteration.)Tj
3.8607 0 Td
(To)Tj
1.338 0 Td
(compute)Tj
/F10 1 Tf
3.7417 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
1.9219 0 Td
(for)Tj
1.3889 0 Td
(all)Tj
/F10 1 Tf
1.1452 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.8788 0 Td
(the)Tj
1.4683 0 Td
(vertices)Tj
3.2428 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(current)Tj
-32.8476 -1.304 Td
(graph)Tj
/F10 1 Tf
2.5341 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 232.1007 297.8078 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 236.6362 294.1795 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(=)Tj
0.7993 0 Td
(\()Tj
/F10 1 Tf
[(\()]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 254.6645 297.8078 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 257.0456 294.1795 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
/F10 1 Tf
0.4478 0 Td
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 266.9669 297.8078 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 269.4047 294.1795 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\))Tj
0.5555 0 Td
(are)Tj
1.4457 0 Td
(first)Tj
1.8085 0 Td
(sorted)Tj
2.7042 0 Td
(in)Tj
1.0375 0 Td
(topological)Tj
4.6318 0 Td
(order)Tj
/F10 1 Tf
2.4208 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 419.811 292.5354 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 425.537 294.1795 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F18 1 Tf
0.9921 0 Td
(.)Tj
0.4308 0 Td
(.)Tj
0.4366 0 Td
(.)Tj
/F15 1 Tf
0.4875 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9865 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 463.2377 292.5354 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 467.2062 294.1795 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
0.4422 0 Td
(Define)Tj
/F10 1 Tf
2.9026 0 Td
[(*)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
1.8539 0 Td
(as)Tj
1.0091 0 Td
(the)Tj
1.4683 0 Td
(number)Tj
-34.3953 -1.2982 Td
(of)Tj
1.0148 0 Td
(paths)Tj
2.3585 0 Td
(ending)Tj
2.999 0 Td
(at)Tj
/F10 1 Tf
0.9524 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.8788 0 Td
(The)Tj
1.7858 0 Td
(vertices)Tj
3.2428 0 Td
(are)Tj
1.4457 0 Td
(visited)Tj
2.8176 0 Td
(in)Tj
1.0374 0 Td
(topological)Tj
4.6375 0 Td
(order)Tj
2.4208 0 Td
(and)Tj
1.7347 0 Td
(the)Tj
1.4683 0 Td
(incoming)Tj
4.0649 0 Td
(edges)Tj
2.4207 0 Td
(into)Tj
/F10 1 Tf
1.8425 0 Td
[()]TJ
/F9 1 Tf
-37.1222 -1.2983 Td
(are)Tj
1.4457 0 Td
(used)Tj
2.0636 0 Td
(to)Tj
1.0262 0 Td
(compute:)Tj
/F10 1 Tf
0 Tc
9.1275 -2.0466 Td
[(*)]TJ
/F15 1 Tf
0.5725 0 Td
()Tj
/F10 1 Tf
[()]TJ
/F15 1 Tf
0.8448 0 Td
()Tj
0.6576 0 Td
()Tj
/F18 1 Tf
1.0488 0 Td
(1)Tj
/F15 1 Tf
0.7257 0 Td
()Tj
/F21 1 Tf
1.3436 0.9468 Td
(X)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 385.0582 237.0897 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F10 1 Tf
[(\r)]TJ
/F20 1 Tf
(;)Tj
/F10 1 Tf
[()]TJ
/F15 1 Tf
1.6441 0 Td
(2)Tj
/F10 1 Tf
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 404.5606 238.8472 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 408.0755 247.748 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[(*)]TJ
/F15 1 Tf
0.5725 0 Td
()Tj
/F10 1 Tf
[(\r)]TJ
/F15 1 Tf
()Tj
14.9669 0 Td
()Tj
/F9 1 Tf
(5)Tj
/F15 1 Tf
()Tj
/F9 1 Tf
-0.004 Tc
-36.3455 -3.2144 Td
(Similarly,)Tj
/F10 1 Tf
4.0252 0 Td
[()]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\),)Tj
2.2563 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(paths)Tj
2.3584 0 Td
(starting)Tj
3.2655 0 Td
(at)Tj
/F10 1 Tf
0.9524 0 Td
[()]TJ
/F9 1 Tf
0.652 0 Td
(is)Tj
0.8447 0 Td
(computed)Tj
4.2689 0 Td
(by)Tj
1.1792 0 Td
(visiting)Tj
3.1521 0 Td
(the)Tj
1.4683 0 Td
(vertices)Tj
3.2428 0 Td
(in)Tj
1.0375 0 Td
(reverse)Tj
-34.605 -1.2983 Td
(topological)Tj
4.6374 0 Td
(order)Tj
2.4208 0 Td
(and)Tj
1.7291 0 Td
(computing.)Tj
/F10 1 Tf
0 Tc
4.7509 -2.0466 Td
[()]TJ
/F15 1 Tf
()Tj
/F10 1 Tf
[()]TJ
/F15 1 Tf
1.542 0 Td
()Tj
0.6576 0 Td
()Tj
/F18 1 Tf
1.0488 0 Td
(1)Tj
/F15 1 Tf
0.7257 0 Td
()Tj
/F21 1 Tf
1.3436 0.9468 Td
(X)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 385.0582 171.496 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
(;)Tj
/F10 1 Tf
1.1149 0 Td
[(\r)]TJ
/F15 1 Tf
(2)Tj
/F10 1 Tf
[(\))]TJ
ET
Q
q
1 j
1 J
0 w
5 0 0 5 404.5606 173.2535 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 408.0755 182.1543 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F15 1 Tf
()Tj
/F10 1 Tf
[(\r)]TJ
/F15 1 Tf
()Tj
15.5394 0 Td
()Tj
/F9 1 Tf
(6)Tj
/F15 1 Tf
()Tj
/F10 1 Tf
-0.004 Tc
-36.3455 -3.2144 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
1.9219 0 Td
(is)Tj
0.8503 0 Td
(then)Tj
2.0183 0 Td
(calculated)Tj
4.2009 0 Td
(for)Tj
1.389 0 Td
(all)Tj
1.1452 0 Td
(vertices)Tj
3.2428 0 Td
(as:)Tj
/F10 1 Tf
0 Tc
-0.5613 -1.8482 Td
[(&)]TJ
/F15 1 Tf
0.669 0 Td
()Tj
/F10 1 Tf
[()]TJ
/F15 1 Tf
0.8391 0 Td
()Tj
0.6633 0 Td
()Tj
/F10 1 Tf
1.0488 0 Td
[(*)]TJ
/F15 1 Tf
0.5726 0 Td
()Tj
/F10 1 Tf
[()]TJ
/F15 1 Tf
0.8447 0 Td
()Tj
0.6009 0 Td
()Tj
/F10 1 Tf
0.4933 0 Td
[()]TJ
/F15 1 Tf
()Tj
/F10 1 Tf
[()]TJ
/F15 1 Tf
1.5419 0 Td
()Tj
/F20 1 Tf
(:)Tj
/F15 1 Tf
14.8648 0 Td
()Tj
/F9 1 Tf
(7)Tj
/F15 1 Tf
()Tj
/F9 1 Tf
-0.004 Tc
-35.1493 -2.2507 Td
(A)Tj
0.9071 0 Td
(vertex)Tj
/F10 1 Tf
2.6589 0 Td
[()]TJ
/F9 1 Tf
0.6519 0 Td
(with)Tj
1.9956 0 Td
(maximum)Tj
/F10 1 Tf
4.3767 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
1.9218 0 Td
(is)Tj
0.8504 0 Td
(removed,)Tj
/F10 1 Tf
3.9685 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 392.0314 112.6488 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 396.6236 109.0204 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8503 0 Td
(updated,)Tj
3.7021 0 Td
(and)Tj
1.7291 0 Td
(the)Tj
1.4683 0 Td
(process)Tj
3.1861 0 Td
(is)Tj
0.8448 0 Td
(repeated)Tj
3.6396 0 Td
(until)Tj
-35.0812 -1.3039 Td
(there)Tj
2.262 0 Td
(are)Tj
1.4513 0 Td
(no)Tj
1.2756 0 Td
(paths)Tj
2.3584 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7269 0 Td
[(')]TJ
/F9 1 Tf
0.6123 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(graph.)Tj
ET
Q
q
0.955 g
1 j
1 J
0 w
200.0001 713.9999 m
576 713.9999 l
576 549.68 l
200.0001 549.68 l
f*
0 g
11.9999 0 0 11.9999 211.9748 698.1165 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(Algorithm)Tj
4.3984 0 Td
(1)Tj
0.7654 0 Td
(DOCKS:)Tj
4.0299 0 Td
(Find)Tj
2.1449 0 Td
(a)Tj
0.7654 0 Td
(compact)Tj
/F7 1 Tf
3.9638 0 Td
(k)Tj
/F0 1 Tf
(-mer)Tj
2.7543 0 Td
(set)Tj
1.5449 0 Td
(hitting)Tj
2.8489 0 Td
(all)Tj
/F7 1 Tf
1.2 0 Td
(L)Tj
/F0 1 Tf
(-long)Tj
-24.4159 -1.096 Td
(sequences)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 223.9937 668.9196 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(1:)Tj
0.924 0 Td
(Generate)Tj
3.8551 0 Td
(a)Tj
0.652 0 Td
(complete)Tj
3.8834 0 Td
(de)Tj
1.1679 0 Td
(Bruijn)Tj
2.7723 0 Td
(graph)Tj
/F10 1 Tf
2.5341 0 Td
[()]TJ
/F9 1 Tf
0.8958 0 Td
(of)Tj
1.0148 0 Td
(order)Tj
/F10 1 Tf
2.4207 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9128 0 Td
(set)Tj
/F10 1 Tf
1.2982 0 Td
[(')]TJ
/F9 1 Tf
0.6123 0 Td
(=)Tj
/F10 1 Tf
0.8051 0 Td
[()]TJ
/F17 1 Tf
0.7426 0 Td
[()]TJ
/F10 1 Tf
0.7937 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
-25.2848 -1.2982 Td
(2:)Tj
0.924 0 Td
(Find)Tj
2.0863 0 Td
(a)Tj
0.6577 0 Td
(decycling)Tj
3.9968 0 Td
(vertex)Tj
2.6589 0 Td
(set)Tj
/F10 1 Tf
1.3039 0 Td
[(")]TJ
/F9 1 Tf
0.8504 0 Td
(using)Tj
2.3924 0 Td
(Mykkeltveit's)Tj
5.5445 0 Td
(algorithm.)Tj
-20.4149 -1.2983 Td
(3:)Tj
0.924 0 Td
(Remove)Tj
3.4696 0 Td
(all)Tj
1.1452 0 Td
(vertices)Tj
3.2428 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[(")]TJ
/F9 1 Tf
0.8504 0 Td
(from)Tj
2.2053 0 Td
(graph)Tj
/F10 1 Tf
2.5342 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
1.1225 0 Td
(resulting)Tj
3.7247 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 443.6787 646.5826 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 446.0598 642.9543 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
-22.2064 -1.3039 Td
(4:)Tj
/F16 1 Tf
0.9241 0 Td
(while)Tj
/F9 1 Tf
2.4491 0 Td
(there)Tj
2.2677 0 Td
(are)Tj
1.4456 0 Td
(still)Tj
1.6385 0 Td
(paths)Tj
2.3584 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7325 0 Td
[(')]TJ
/F16 1 Tf
0.6123 0 Td
(do)Tj
/F9 1 Tf
-15.443 -1.2982 Td
(5:)Tj
1.9219 0 Td
(Calculate)Tj
/F10 1 Tf
3.9174 0 Td
[()]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.9162 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
0.8221 0 Td
(and)Tj
/F10 1 Tf
1.7348 0 Td
[(*)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.7347 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
0.8278 0 Td
(for)Tj
1.3833 0 Td
(each)Tj
2.0295 0 Td
(vertex)Tj
/F10 1 Tf
2.6589 0 Td
[()]TJ
/F9 1 Tf
0.652 0 Td
(and)Tj
1.7291 0 Td
(0)Tj
/F15 1 Tf
0 Tc
0.6973 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.4875 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[(')]TJ
/F9 1 Tf
(.)Tj
-24.4967 -1.2983 Td
(6:)Tj
1.9219 0 Td
(Calculate)Tj
/F10 1 Tf
3.9174 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.8085 0 Td
[(')]TJ
/F9 1 Tf
(\))Tj
0.9524 0 Td
(for)Tj
1.389 0 Td
(each)Tj
2.0296 0 Td
(vertex)Tj
/F10 1 Tf
2.6532 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
-14.672 -1.3039 Td
(7:)Tj
1.9219 0 Td
(Remove)Tj
3.4695 0 Td
(a)Tj
0.6577 0 Td
(vertex)Tj
2.6532 0 Td
(with)Tj
1.9956 0 Td
(maximum)Tj
4.3766 0 Td
(hitting)Tj
2.8913 0 Td
(number)Tj
3.4186 0 Td
(from)Tj
/F10 1 Tf
2.2052 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 466.6393 594.5385 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 469.0204 590.9102 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4478 0 Td
(and)Tj
1.7291 0 Td
(add)Tj
1.7065 0 Td
(it)Tj
0.788 0 Td
(to)Tj
1.0262 0 Td
(set)Tj
/F10 1 Tf
1.3039 0 Td
[(")]TJ
/F9 1 Tf
(.)Tj
-31.504 -1.2982 Td
(8:)Tj
/F16 1 Tf
0.9241 0 Td
(end)Tj
1.7575 0 Td
(while)Tj
/F9 1 Tf
-2.6816 -1.2983 Td
(9:)Tj
0.9241 0 Td
(Output)Tj
3.1351 0 Td
(set)Tj
/F10 1 Tf
1.3039 0 Td
[(")]TJ
/F9 1 Tf
(.)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 169.285 23.6976 re
W* n
q
169.2283 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 450.4818 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Compact)Tj
4.1669 0 Td
(universal)Tj
/F7 1 Tf
4.1386 0 Td
(k)Tj
/F0 1 Tf
(-mer)Tj
2.7355 0 Td
(hitting)Tj
2.8346 0 Td
(sets)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
142.5827 34.9228 m
295.8236 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(Computationa)Tj
6.1229 0 Td
(l)Tj
0.4322 0 Td
(Biology)Tj
3.4371 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https:/)Tj
2.6788 0 Td
(/doi.org/10.13)Tj
6.0094 0 Td
(71/journal.p)Tj
5.1166 0 Td
(cbi.1005777)Tj
0 g
6.3497 0 Td
(October)Tj
3.7276 0 Td
(2,)Tj
1.0346 0 Td
(2017)Tj
26.901 0 Td
(6)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
117 0 obj
<>stream
endstream
endobj
118 0 obj
<>stream
endstream
endobj
119 0 obj
<>stream
endstream
endobj
120 0 obj
<>stream
endstream
endobj
121 0 obj
<>stream
endstream
endobj
122 0 obj
<>stream
BT
66.402 0 Td
(15)Tj
ET
Q
endstream
endobj
123 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 17 0 R/Annots 124 0 R/Contents 125 0 R/TrimBox[0 0 612 792]>>
endobj
124 0 obj
[126 0 R]
endobj
126 0 obj
<>/Border[0 0 0]/A 127 0 R>>
endobj
127 0 obj
<>
endobj
125 0 obj
[128 0 R 129 0 R 130 0 R 131 0 R 132 0 R]
endobj
128 0 obj
<>stream
q
1 j
1 J
0 w
10 0 0 10 211.9748 518.1165 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(Computing)Tj
/F10 1 Tf
4.8358 0 Td
[()]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
2.0296 0 Td
(for)Tj
1.3833 0 Td
(all)Tj
/F10 1 Tf
1.1509 0 Td
[()]TJ
/F9 1 Tf
0.6519 0 Td
(requires)Tj
3.4753 0 Td
(visiting)Tj
3.1464 0 Td
(each)Tj
2.0296 0 Td
(edge)Tj
2.058 0 Td
(in)Tj
1.0374 0 Td
(the)Tj
1.4684 0 Td
(graph)Tj
2.5341 0 Td
(once,)Tj
2.3471 0 Td
(and)Tj
1.7348 0 Td
(hence)Tj
2.5625 0 Td
(takes)Tj
/F10 1 Tf
-33.6413 -1.3039 Td
[()]TJ
/F9 1 Tf
(\(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 222.1228 509.5559 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 233.4614 505.0771 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\).)Tj
0.788 0 Td
(The)Tj
1.7801 0 Td
(time)Tj
2.0296 0 Td
(for)Tj
1.389 0 Td
(computing)Tj
/F10 1 Tf
4.5921 0 Td
[(*)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
1.8538 0 Td
(for)Tj
1.3833 0 Td
(all)Tj
/F10 1 Tf
1.1452 0 Td
[()]TJ
/F9 1 Tf
0.6576 0 Td
(is)Tj
0.8448 0 Td
(the)Tj
1.474 0 Td
(same.)Tj
2.4831 0 Td
(Hence,)Tj
/F10 1 Tf
3.0274 0 Td
[(&)]TJ
/F9 1 Tf
0.8107 0 Td
(is)Tj
0.8504 0 Td
(computable)Tj
4.9266 0 Td
(in)Tj
/F10 1 Tf
-33.3805 -1.2982 Td
[()]TJ
/F9 1 Tf
(\(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 222.1228 496.5165 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 233.4614 492.0944 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\))Tj
0.5612 0 Td
(time.)Tj
2.2564 0 Td
(Computing)Tj
4.8358 0 Td
(the)Tj
1.4684 0 Td
(longest)Tj
3.067 0 Td
(path)Tj
2.0013 0 Td
(in)Tj
1.0318 0 Td
(a)Tj
0.6576 0 Td
(DAG)Tj
2.3528 0 Td
(\(step)Tj
2.16 0 Td
(4\))Tj
1.0374 0 Td
(also)Tj
1.7688 0 Td
(requires)Tj
/F10 1 Tf
3.4696 0 Td
[()]TJ
/F9 1 Tf
(\(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 522.2551 496.5165 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 533.6503 492.0944 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\).)Tj
0.7823 0 Td
(If)Tj
/F10 1 Tf
0.8504 0 Td
[()]TJ
/F9 1 Tf
0.6973 0 Td
(ver-)Tj
-35.6935 -1.2982 Td
(tices)Tj
1.9899 0 Td
(are)Tj
1.4513 0 Td
(removed,)Tj
3.9742 0 Td
(then)Tj
2.0182 0 Td
(the)Tj
1.4684 0 Td
(total)Tj
2.0012 0 Td
(runtime)Tj
3.4809 0 Td
(for)Tj
1.3833 0 Td
(this)Tj
1.6725 0 Td
(algorithm)Tj
4.1612 0 Td
(is)Tj
/F10 1 Tf
0.8447 0 Td
[()]TJ
/F9 1 Tf
(\(\(1)Tj
2.0693 0 Td
(+)Tj
/F10 1 Tf
0.7994 0 Td
[()]TJ
/F9 1 Tf
(\)|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 493.1149 483.5338 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 504.4535 479.1118 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\),)Tj
0.788 0 Td
(a)Tj
0.6519 0 Td
(factor)Tj
2.5455 0 Td
(of)Tj
/F22 1 Tf
1.0148 0 Td
( )Tj
/F9 1 Tf
(\()Tj
/F10 1 Tf
[(')]TJ
/F9 1 Tf
(\))Tj
-35.4441 -1.3039 Td
(faster)Tj
2.3925 0 Td
(than)Tj
2.0296 0 Td
(the)Tj
1.4683 0 Td
(DOCKS)Tj
3.5206 0 Td
(algorithm.)Tj
4.3823 0 Td
(The)Tj
1.7802 0 Td
(space)Tj
2.3811 0 Td
(complexity)Tj
4.6374 0 Td
(is)Tj
0.8504 0 Td
(also)Tj
1.7688 0 Td
(smaller,)Tj
/F10 1 Tf
3.3449 0 Td
[()]TJ
/F9 1 Tf
(\(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 507.685 470.5511 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 519.0803 466.0724 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\))Tj
0.5612 0 Td
(vs.)Tj
/F10 1 Tf
-32.4677 -1.2982 Td
[()]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[(')]TJ
/F9 1 Tf
(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 226.0346 457.5118 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 237.4299 453.0897 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(\))Tj
0.5555 0 Td
(for)Tj
1.389 0 Td
(DOCKS.)Tj
-0.007 Tc
-4.4899 -1.2982 Td
(In)Tj
1.1055 0 Td
(addition)Tj
3.5715 0 Td
(to)Tj
1.0205 0 Td
(shorter)Tj
3.0614 0 Td
(runtimes)Tj
3.8097 0 Td
(and)Tj
1.7234 0 Td
(decreased)Tj
4.1103 0 Td
(memory)Tj
3.5943 0 Td
(usage,)Tj
2.6418 0 Td
(this)Tj
1.6611 0 Td
(heuristic)Tj
3.6567 0 Td
(offers)Tj
2.4435 0 Td
(one)Tj
1.6894 0 Td
(more)Tj
-35.2854 -1.3039 Td
(advantage)Tj
4.2122 0 Td
(over)Tj
1.9616 0 Td
(the)Tj
1.4626 0 Td
(original)Tj
3.3052 0 Td
(DOCKS)Tj
3.4979 0 Td
(algorithm.)Tj
4.354 0 Td
(The)Tj
1.7688 0 Td
(vertex)Tj
2.6419 0 Td
(removal)Tj
3.4526 0 Td
(choice)Tj
2.7779 0 Td
(is)Tj
0.8391 0 Td
(independent)Tj
5.244 0 Td
(of)Tj
/F10 1 Tf
1.0092 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
-36.527 -1.2983 Td
(The)Tj
1.7745 0 Td
(value)Tj
2.2903 0 Td
(of)Tj
/F10 1 Tf
1.0091 0 Td
[()]TJ
/F9 1 Tf
0.7427 0 Td
(only)Tj
1.9672 0 Td
(determines)Tj
4.6545 0 Td
(when)Tj
2.3867 0 Td
(the)Tj
1.4627 0 Td
(algorithm)Tj
4.1272 0 Td
(terminates.)Tj
4.6602 0 Td
(Thus,)Tj
2.4604 0 Td
(hitting)Tj
2.8687 0 Td
(sets)Tj
1.6497 0 Td
(for)Tj
1.3776 0 Td
(all)Tj
1.1396 0 Td
(values)Tj
-34.5711 -1.2983 Td
(of)Tj
/F10 1 Tf
0.9978 0 Td
[()]TJ
/F9 1 Tf
0.7427 0 Td
(or)Tj
1.0828 0 Td
(larger)Tj
2.5057 0 Td
(can)Tj
1.6101 0 Td
(be)Tj
1.1339 0 Td
(computed)Tj
4.2349 0 Td
(in)Tj
1.0261 0 Td
(one)Tj
1.6781 0 Td
(run.)Tj
1.8766 0 Td
(This)Tj
1.9672 0 Td
(is)Tj
0.8334 0 Td
(in)Tj
1.0204 0 Td
(contrast)Tj
3.4356 0 Td
(with)Tj
1.9729 0 Td
(DOCKS,)Tj
3.719 0 Td
(in)Tj
1.0205 0 Td
(which)Tj
2.6305 0 Td
(the)Tj
1.4514 0 Td
(hitting)Tj
-34.9396 -1.2982 Td
(number)Tj
3.3959 0 Td
(of)Tj
1.0091 0 Td
(each)Tj
2.0182 0 Td
(vertex)Tj
2.6419 0 Td
(depends)Tj
3.5263 0 Td
(on)Tj
/F10 1 Tf
1.2699 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9637 0 Td
(and)Tj
1.7235 0 Td
(so)Tj
1.0828 0 Td
(DOCKS)Tj
3.498 0 Td
(must)Tj
2.2166 0 Td
(be)Tj
1.1452 0 Td
(run)Tj
1.6554 0 Td
(for)Tj
1.3777 0 Td
(each)Tj
2.0182 0 Td
(desired)Tj
3.1011 0 Td
(value)Tj
2.2904 0 Td
(of)Tj
/F10 1 Tf
1.0091 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
-0.004 Tc
-34.7467 -1.3039 Td
(Finally,)Tj
3.1746 0 Td
(in)Tj
1.0318 0 Td
(order)Tj
2.4208 0 Td
(to)Tj
1.0261 0 Td
(calculate)Tj
3.6794 0 Td
(the)Tj
1.4683 0 Td
(hitting)Tj
2.8914 0 Td
(set)Tj
1.3039 0 Td
(for)Tj
1.3833 0 Td
(even)Tj
2.0749 0 Td
(larger)Tj
/F10 1 Tf
2.5285 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9128 0 Td
(we)Tj
1.3266 0 Td
(can)Tj
1.627 0 Td
(further)Tj
3.0274 0 Td
(speed)Tj
2.4718 0 Td
(up)Tj
-33.5449 -1.2983 Td
(DOCKSany)Tj
4.9492 0 Td
(as)Tj
1.0148 0 Td
(follows.)Tj
3.2882 0 Td
(In)Tj
1.1055 0 Td
(the)Tj
1.474 0 Td
(DOCKSanyX)Tj
5.6012 0 Td
(heuristic,)Tj
3.9175 0 Td
(the)Tj
1.4683 0 Td
(top)Tj
/F10 1 Tf
1.542 0 Td
[(")]TJ
/F9 1 Tf
0.8504 0 Td
(vertices,)Tj
3.4696 0 Td
(ranked)Tj
3.0217 0 Td
(by)Tj
1.1792 0 Td
(the)Tj
1.474 0 Td
(hitting)Tj
-34.3556 -1.2983 Td
(number)Tj
/F10 1 Tf
3.4186 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\),)Tj
2.1486 0 Td
(are)Tj
1.4456 0 Td
(removed)Tj
3.7474 0 Td
(\(in)Tj
1.3776 0 Td
(step)Tj
1.8198 0 Td
(7\))Tj
1.0375 0 Td
(in)Tj
1.0318 0 Td
(each)Tj
2.0296 0 Td
(iteration.)Tj
3.8608 0 Td
(This)Tj
1.9899 0 Td
(can)Tj
1.6271 0 Td
(shorten)Tj
3.2541 0 Td
(the)Tj
1.4684 0 Td
(running)Tj
3.4979 0 Td
(time)Tj
2.0296 0 Td
(of)Tj
-35.7843 -1.3039 Td
(each)Tj
2.0296 0 Td
(iteration)Tj
3.6339 0 Td
(by)Tj
1.1792 0 Td
(a)Tj
0.6577 0 Td
(factor)Tj
2.5398 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[(")]TJ
/F9 1 Tf
(,)Tj
1.0771 0 Td
(but)Tj
1.5534 0 Td
(may)Tj
1.9276 0 Td
(produce)Tj
3.5206 0 Td
(larger)Tj
2.5285 0 Td
(hitting)Tj
2.8913 0 Td
(set)Tj
1.3039 0 Td
(solutions.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 299.9055 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(An)Tj
1.4315 0 Td
(integer)Tj
3.2362 0 Td
(linear)Tj
2.6221 0 Td
(programming)Tj
6.0425 0 Td
(\(ILP\))Tj
2.367 0 Td
(formulation)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 282.8976 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(To)Tj
1.3379 0 Td
(investigate)Tj
4.4617 0 Td
(whether)Tj
3.4753 0 Td
(optimal)Tj
3.3108 0 Td
(solutions)Tj
3.8438 0 Td
(can)Tj
1.6214 0 Td
(be)Tj
1.1508 0 Td
(found)Tj
2.6192 0 Td
(practically,)Tj
4.5638 0 Td
(we)Tj
1.3266 0 Td
(formulate)Tj
4.1385 0 Td
(the)Tj
1.4684 0 Td
(problem)Tj
-33.3182 -1.2982 Td
(of)Tj
1.0147 0 Td
(the)Tj
1.4684 0 Td
(minimal)Tj
3.6226 0 Td
(universal)Tj
/F10 1 Tf
3.8551 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6476 0 Td
(hitting)Tj
2.8913 0 Td
(set)Tj
1.3039 0 Td
(as)Tj
1.0148 0 Td
(an)Tj
1.2019 0 Td
(integer)Tj
3.0217 0 Td
(linear)Tj
2.5115 0 Td
(program)Tj
3.702 0 Td
(\(ILP\).)Tj
2.5625 0 Td
(In)Tj
1.1112 0 Td
(the)Tj
1.4683 0 Td
(ILP)Tj
1.6555 0 Td
(for-)Tj
-35.053 -1.2983 Td
(mulation)Tj
3.8664 0 Td
(there)Tj
2.2677 0 Td
(are)Tj
1.4456 0 Td
(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 287.6031 261.3543 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 293.2724 256.9322 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(binary)Tj
2.8006 0 Td
(variables)Tj
/F10 1 Tf
3.719 0 Td
[(+)]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 363.1181 255.2314 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 367.3133 256.9322 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(representing)Tj
5.2383 0 Td
(whether)Tj
3.481 0 Td
(vertex)Tj
/F10 1 Tf
2.6532 0 Td
[()]TJ
/F9 1 Tf
0.4875 0 Td
(is)Tj
0.8504 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.474 0 Td
(solution)Tj
3.481 0 Td
(hit-)Tj
-35.4271 -1.3039 Td
(ting)Tj
1.7971 0 Td
(set.)Tj
1.5307 0 Td
(There)Tj
2.5739 0 Td
(are)Tj
1.4513 0 Td
(also)Tj
1.7688 0 Td
(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 302.9669 248.3716 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 308.6362 243.8929 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(variables)Tj
/F10 1 Tf
3.719 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 351.0992 242.2488 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 355.2944 243.8929 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(representing)Tj
5.244 0 Td
(an)Tj
1.2019 0 Td
(upper)Tj
2.5738 0 Td
(bound)Tj
2.8403 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4684 0 Td
(number)Tj
3.4185 0 Td
(of)Tj
1.0148 0 Td
(edges)Tj
-34.5653 -1.2982 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.474 0 Td
(longest)Tj
3.067 0 Td
(path)Tj
1.9956 0 Td
(ending)Tj
3.0047 0 Td
(at)Tj
0.9525 0 Td
(vertex)Tj
/F10 1 Tf
2.6532 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.7143 0 Td
(The)Tj
1.78 0 Td
(constraints)Tj
4.6432 0 Td
(on)Tj
/F10 1 Tf
1.2755 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 431.2062 229.2661 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 435.4015 230.9102 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(guarantee)Tj
4.1442 0 Td
(that)Tj
1.7801 0 Td
(the)Tj
1.4684 0 Td
(vertices)Tj
3.2428 0 Td
(chosen)Tj
-34.1742 -1.2982 Td
(remove)Tj
3.2201 0 Td
(all)Tj
/F10 1 Tf
1.1452 0 Td
[(')]TJ
/F9 1 Tf
(-long)Tj
2.7269 0 Td
(paths)Tj
2.3584 0 Td
(\()Tj
/F10 1 Tf
[(')]TJ
/F9 1 Tf
0.9525 0 Td
(=)Tj
/F10 1 Tf
0.7993 0 Td
[()]TJ
/F17 1 Tf
0.7484 0 Td
[()]TJ
/F10 1 Tf
0.7937 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
1.0205 0 Td
(from)Tj
2.211 0 Td
(the)Tj
1.4683 0 Td
(graph.)Tj
2.7609 0 Td
(The)Tj
1.7802 0 Td
(ILP)Tj
1.6553 0 Td
(is)Tj
0.8504 0 Td
(defined)Tj
3.2258 0 Td
(as)Tj
1.0148 0 Td
(follows:)Tj
/F17 1 Tf
0 Tc
-21.5544 -3.7757 Td
[(\n)2()1()]TJ
1.5987 0 Td
[()1(\n)2(\r)-2()]TJ
2.4321 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
14 0 0 14 324.2834 193.4362 cm
BT
/F21 1 Tf
1 TL
0 0 Td
(X)Tj
ET
Q
q
1 j
1 J
0 w
8.3997 0 0 8.3997 327.2881 196.9511 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(j)Tj
/F19 1 Tf
(S)Tj
/F15 1 Tf
(j)Tj
ET
Q
q
1 j
1 J
0 w
7 0 0 7 337.4362 200.5795 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
8.3997 0 0 8.3997 327.8551 165.4866 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F15 1 Tf
()Tj
/F18 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 344.4094 180.17 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[(+)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 349.0582 177.6755 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 351.2125 180.17 cm
BT
/F20 1 Tf
1 TL
0 0 Td
(;)Tj
/F17 1 Tf
-7.9426 -3.1577 Td
[()5()]TJ
0.8731 0 Td
[()11()-5()-6()]TJ
1.5704 0 Td
[()]TJ
0.4025 0 Td
[()6()]TJ
1.0771 0 Td
[()]TJ
/F10 1 Tf
1.3267 0 Td
[(+)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 328.9889 146.0976 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 333.8645 148.5921 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(2)Tj
0.9354 0 Td
(f)Tj
/F18 1 Tf
(0)Tj
/F20 1 Tf
(;)Tj
/F18 1 Tf
1.44 0 Td
(1)Tj
/F15 1 Tf
(g)Tj
/F20 1 Tf
(;)Tj
/F18 1 Tf
8.4415 0 Td
(1)Tj
/F15 1 Tf
0.7823 0 Td
()Tj
/F10 1 Tf
1.0489 0 Td
[()]TJ
/F15 1 Tf
0.5499 0 Td
()Tj
1.0488 0 Td
(j)Tj
/F19 1 Tf
(S)Tj
/F15 1 Tf
(j)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 488.4094 153.8078 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 324.2834 131.6409 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(0)Tj
/F15 1 Tf
0.7766 0 Td
()Tj
/F10 1 Tf
1.0545 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 347.8677 129.1464 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 352.8 131.6409 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F20 1 Tf
1.0488 0 Td
(`)Tj
/F15 1 Tf
0.6292 0 Td
( )Tj
/F18 1 Tf
0.9922 0 Td
(1)Tj
/F20 1 Tf
(;)Tj
/F18 1 Tf
6.2532 0 Td
(1)Tj
/F15 1 Tf
0.7823 0 Td
()Tj
/F10 1 Tf
1.0488 0 Td
[()]TJ
/F15 1 Tf
0.5499 0 Td
()Tj
1.0489 0 Td
(j)Tj
/F19 1 Tf
(S)Tj
/F15 1 Tf
(j)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 488.4094 136.8 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 563.4708 165.4866 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F9 1 Tf
(8)Tj
/F15 1 Tf
()Tj
/F10 1 Tf
-24.236 -6.0944 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 326.3811 102.0472 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 332.4472 104.5417 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F18 1 Tf
1.0488 0 Td
(1)Tj
/F15 1 Tf
0.72 0 Td
()Tj
/F10 1 Tf
0.9921 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 365.3858 102.0472 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[(\r)]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 371.3385 104.5417 cm
BT
/F15 1 Tf
1 TL
0 0 Td
( )Tj
/F20 1 Tf
0.9921 0 Td
(`)Tj
/F10 1 Tf
[(+)]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 389.9905 102.0472 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 393.2787 104.5417 cm
BT
/F20 1 Tf
1 TL
0 0 Td
(;)Tj
/F15 1 Tf
4.9209 0 Td
()Tj
/F10 1 Tf
[(\r)]TJ
/F20 1 Tf
(;)Tj
/F10 1 Tf
1.3549 0 Td
[()]TJ
/F15 1 Tf
0.4536 0 Td
()Tj
0.6633 0 Td
(2)Tj
/F10 1 Tf
0.9354 0 Td
[(\))]TJ
/F15 1 Tf
8.691 0 Td
()Tj
/F9 1 Tf
(9)Tj
/F15 1 Tf
()Tj
ET
Q
q
0.955 g
1 j
1 J
0 w
200.0001 713.9999 m
576 713.9999 l
576 549.68 l
200.0001 549.68 l
f*
0 g
11.9999 0 0 11.9999 211.9748 698.1165 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(Algorithm)Tj
4.3984 0 Td
(2)Tj
0.7654 0 Td
(DOCKSany:)Tj
5.6221 0 Td
(A)Tj
0.8834 0 Td
(faster)Tj
2.6977 0 Td
(heuristic)Tj
3.8977 0 Td
(for)Tj
1.3748 0 Td
(a)Tj
0.7701 0 Td
(compact)Tj
/F7 1 Tf
3.9638 0 Td
(k)Tj
/F0 1 Tf
(-mer)Tj
2.7496 0 Td
(set)Tj
-27.123 -1.096 Td
(hitting)Tj
2.8535 0 Td
(all)Tj
/F7 1 Tf
1.2 0 Td
(L)Tj
/F0 1 Tf
(-long)Tj
2.9575 0 Td
(sequences)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 223.9937 668.9196 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(1:)Tj
0.924 0 Td
(Generate)Tj
3.8551 0 Td
(a)Tj
0.652 0 Td
(complete)Tj
3.8834 0 Td
(de)Tj
1.1679 0 Td
(Bruijn)Tj
2.7723 0 Td
(graph)Tj
/F10 1 Tf
2.5341 0 Td
[()]TJ
/F9 1 Tf
0.8958 0 Td
(of)Tj
1.0148 0 Td
(order)Tj
/F10 1 Tf
2.4207 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9128 0 Td
(set)Tj
/F10 1 Tf
1.2982 0 Td
[(')]TJ
/F9 1 Tf
0.6123 0 Td
(=)Tj
/F10 1 Tf
0.8051 0 Td
[()]TJ
/F17 1 Tf
0.7426 0 Td
[()]TJ
/F10 1 Tf
0.7937 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
-25.2848 -1.2982 Td
(2:)Tj
0.924 0 Td
(Find)Tj
2.0863 0 Td
(a)Tj
0.6577 0 Td
(decycling)Tj
3.9968 0 Td
(vertex)Tj
2.6589 0 Td
(set)Tj
/F10 1 Tf
1.3039 0 Td
[(")]TJ
/F9 1 Tf
0.8504 0 Td
(using)Tj
2.3924 0 Td
(Mykkeltveit's)Tj
5.5445 0 Td
(algorithm.)Tj
-20.4149 -1.2983 Td
(3:)Tj
0.924 0 Td
(Remove)Tj
3.4696 0 Td
(all)Tj
1.1452 0 Td
(vertices)Tj
3.2428 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[(")]TJ
/F9 1 Tf
0.8504 0 Td
(from)Tj
2.2053 0 Td
(graph)Tj
/F10 1 Tf
2.5342 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
1.1225 0 Td
(resulting)Tj
3.7247 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 443.6787 646.5826 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 446.0598 642.9543 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
-22.2064 -1.3039 Td
(4:)Tj
/F16 1 Tf
0.9241 0 Td
(while)Tj
/F9 1 Tf
2.4491 0 Td
(there)Tj
2.2677 0 Td
(are)Tj
1.4456 0 Td
(still)Tj
1.6385 0 Td
(paths)Tj
2.3584 0 Td
(of)Tj
1.0148 0 Td
(length)Tj
/F10 1 Tf
2.7325 0 Td
[(')]TJ
/F16 1 Tf
0.6123 0 Td
(do)Tj
/F9 1 Tf
-15.443 -1.2982 Td
(5:)Tj
1.9219 0 Td
(Calculate)Tj
/F10 1 Tf
3.9174 0 Td
[()]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
2.0296 0 Td
(and)Tj
/F10 1 Tf
1.7291 0 Td
[(*)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
1.8539 0 Td
(at)Tj
0.9524 0 Td
(each)Tj
2.0239 0 Td
(vertex)Tj
/F10 1 Tf
2.6589 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
-17.0871 -1.2983 Td
(6:)Tj
1.9219 0 Td
(Calculate)Tj
3.9174 0 Td
(the)Tj
1.4683 0 Td
(number)Tj
/F10 1 Tf
3.4186 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
1.9276 0 Td
(of)Tj
1.0148 0 Td
(paths)Tj
2.3584 0 Td
(passing)Tj
3.1691 0 Td
(through)Tj
3.4468 0 Td
(each)Tj
2.0296 0 Td
(vertex)Tj
/F10 1 Tf
2.6532 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
-27.3257 -1.3039 Td
(7:)Tj
1.9219 0 Td
(Remove)Tj
3.4695 0 Td
(a)Tj
0.6577 0 Td
(vertex)Tj
/F10 1 Tf
2.6532 0 Td
[()]TJ
/F9 1 Tf
0.6519 0 Td
(with)Tj
2.0013 0 Td
(maximum)Tj
/F10 1 Tf
4.371 0 Td
[(&)]TJ
/F9 1 Tf
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(\))Tj
1.9275 0 Td
(from)Tj
/F10 1 Tf
2.2054 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
6.9998 0 0 6.9998 429.3354 594.5385 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(0)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 431.7165 590.9102 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4422 0 Td
(and)Tj
1.7347 0 Td
(add)Tj
1.7065 0 Td
(it)Tj
0.788 0 Td
(to)Tj
1.0205 0 Td
(set)Tj
/F10 1 Tf
1.3039 0 Td
[(")]TJ
/F9 1 Tf
(.)Tj
-27.7679 -1.2982 Td
(8:)Tj
/F16 1 Tf
0.9241 0 Td
(end)Tj
1.7575 0 Td
(while)Tj
/F9 1 Tf
-2.6816 -1.2983 Td
(9:)Tj
0.9241 0 Td
(Output)Tj
3.1351 0 Td
(set)Tj
/F10 1 Tf
1.3039 0 Td
[(")]TJ
/F9 1 Tf
(.)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 169.285 23.6976 re
W* n
q
169.2283 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 450.4818 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Compact)Tj
4.1669 0 Td
(universal)Tj
/F7 1 Tf
4.1386 0 Td
(k)Tj
/F0 1 Tf
(-mer)Tj
2.7355 0 Td
(hitting)Tj
2.8346 0 Td
(sets)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
142.5827 34.9228 m
295.8236 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(Computationa)Tj
6.1229 0 Td
(l)Tj
0.4322 0 Td
(Biology)Tj
3.4371 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https:/)Tj
2.6788 0 Td
(/doi.org/10.13)Tj
6.0094 0 Td
(71/journal.p)Tj
5.1166 0 Td
(cbi.1005777)Tj
0 g
6.3497 0 Td
(October)Tj
3.7276 0 Td
(2,)Tj
1.0346 0 Td
(2017)Tj
26.901 0 Td
(7)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
129 0 obj
<>stream
endstream
endobj
130 0 obj
<>stream
endstream
endobj
131 0 obj
<>stream
endstream
endobj
132 0 obj
<>stream
BT
66.402 0 Td
(15)Tj
ET
Q
endstream
endobj
133 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 17 0 R/Annots 135 0 R/Contents 136 0 R/TrimBox[0 0 612 792]>>
endobj
135 0 obj
[137 0 R 138 0 R 139 0 R 140 0 R 141 0 R 142 0 R 143 0 R 144 0 R 145 0 R 146 0 R]
endobj
137 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.s002)>>
endobj
138 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.e016)>>
endobj
139 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref016)>>
endobj
140 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref017)>>
endobj
141 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.t001)>>
endobj
142 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref019)>>
endobj
143 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref020)>>
endobj
144 0 obj
<>/Border[0 0 0]/Dest(Lpcbi.1005777.t001)>>
endobj
145 0 obj
<>/Border[0 0 0]/A 147 0 R>>
endobj
147 0 obj
<>
endobj
146 0 obj
<>/Border[0 0 0]/A 148 0 R>>
endobj
148 0 obj
<>
endobj
136 0 obj
[149 0 R 150 0 R 151 0 R 152 0 R 153 0 R 154 0 R 155 0 R 156 0 R 157 0 R 158 0 R 159 0 R 160 0 R 161 0 R 162 0 R]
endobj
149 0 obj
<>stream
q
0.83 0.64 0.02 0 k
425.7638 680.315 m
455.4709 680.315 l
h
f*
278.5323 432 m
301.0394 432 l
h
f*
389.8772 311.9244 m
399.4016 311.9244 l
h
f*
315.8362 239.6976 m
325.3039 239.6976 l
h
f*
211.9748 213.6756 m
241.2283 213.6756 l
h
f*
469.2472 174.6709 m
478.7717 174.6709 l
h
f*
547.7102 174.6709 m
557.2346 174.6709 l
h
f*
0 g
1 j
1 J
0 w
10 0 0 10 211.9748 707.4141 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(Here)Tj
/F10 1 Tf
2.211 0 Td
[(\))]TJ
/F9 1 Tf
0.7653 0 Td
(contains)Tj
3.6113 0 Td
(all)Tj
1.1452 0 Td
(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 301.0393 711.8362 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 314.6456 707.4141 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(possible)Tj
3.4072 0 Td
(edges.)Tj
2.6475 0 Td
(The)Tj
1.7802 0 Td
(constraint)Tj
4.2802 0 Td
(on)Tj
1.2756 0 Td
(edge)Tj
2.058 0 Td
(\()Tj
/F10 1 Tf
[(\r)]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.3152 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
0.9922 0 Td
(requires)Tj
3.4752 0 Td
(that)Tj
1.7745 0 Td
(if)Tj
/F10 1 Tf
0.7767 0 Td
[()]TJ
/F9 1 Tf
0.6519 0 Td
(is)Tj
-35.8976 -1.3039 Td
(not)Tj
1.5704 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(set)Tj
1.3039 0 Td
(then)Tj
/F10 1 Tf
2.0183 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 279.2692 692.7307 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 284.7118 694.3748 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9921 0 Td
(1)Tj
0.6973 0 Td
(+)Tj
/F10 1 Tf
0.7994 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 314.8724 692.7307 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[(\r)]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 318.8409 694.3748 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
0.4422 0 Td
(The)Tj
1.7858 0 Td
(validity)Tj
3.1691 0 Td
(of)Tj
1.0148 0 Td
(this)Tj
1.6724 0 Td
(formulation)Tj
5.0343 0 Td
(is)Tj
0.8504 0 Td
(proven)Tj
3.0387 0 Td
(in)Tj
1.0375 0 Td
(the)Tj
1.4683 0 Td
(Appendix)Tj
4.1726 0 Td
(\(see)Tj
-35.5688 -1.2982 Td
(Appendix,)Tj
4.3937 0 Td
(Subsection)Tj
4.558 0 Td
(Validity)Tj
3.4128 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4684 0 Td
(ILP)Tj
1.6554 0 Td
(formulation)Tj
5.04 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0318 0 Td
(S1)Tj
1.1735 0 Td
(Text)Tj
0 g
(\).)Tj
-22.5522 -1.2983 Td
(The)Tj
1.7858 0 Td
(number)Tj
3.4186 0 Td
(of)Tj
1.0148 0 Td
(variables)Tj
3.719 0 Td
(and)Tj
1.729 0 Td
(constraints)Tj
4.6375 0 Td
(grows)Tj
2.6078 0 Td
(exponentially)Tj
5.6013 0 Td
(in)Tj
/F10 1 Tf
1.0374 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9071 0 Td
(making)Tj
3.2542 0 Td
(it)Tj
0.7823 0 Td
(hard)Tj
2.0806 0 Td
(to)Tj
1.0262 0 Td
(use)Tj
1.5307 0 Td
(for)Tj
/F10 1 Tf
-36.3285 -1.2982 Td
[()]TJ
/F20 1 Tf
0 Tc
0.686 0 Td
(>)Tj
/F9 1 Tf
-0.004 Tc
0.9921 0 Td
(7.)Tj
0.9184 0 Td
(However,)Tj
4.0762 0 Td
(the)Tj
1.4683 0 Td
(ILP)Tj
1.6611 0 Td
(solver)Tj
2.5794 0 Td
(can)Tj
1.6271 0 Td
(start)Tj
1.9843 0 Td
(from)Tj
2.2053 0 Td
(a)Tj
0.652 0 Td
(feasible)Tj
3.1747 0 Td
(solution)Tj
3.481 0 Td
(produced)Tj
4.0478 0 Td
(by)Tj
1.1792 0 Td
(one)Tj
1.7008 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
-33.4485 -1.304 Td
(DOCKS)Tj
3.5149 0 Td
(algorithms)Tj
4.5184 0 Td
(and)Tj
1.7291 0 Td
(improve)Tj
3.5829 0 Td
(that)Tj
1.7745 0 Td
(solution)Tj
3.4866 0 Td
(for)Tj
1.3833 0 Td
(a)Tj
0.6519 0 Td
(limited)Tj
3.0728 0 Td
(set)Tj
1.3039 0 Td
(time.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 612.0566 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(Handling)Tj
4.1055 0 Td
(larger)Tj
/F7 1 Tf
2.7402 0 Td
(k)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 595.1055 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(The)Tj
1.7801 0 Td
(DOCKS)Tj
3.5149 0 Td
(variants)Tj
3.3902 0 Td
(described)Tj
4.0536 0 Td
(above)Tj
2.5455 0 Td
(have)Tj
2.0579 0 Td
(exponential)Tj
4.8982 0 Td
(dependence)Tj
5.0117 0 Td
(in)Tj
/F10 1 Tf
1.0318 0 Td
[()]TJ
/F9 1 Tf
0.6859 0 Td
(in)Tj
1.0375 0 Td
(both)Tj
2.058 0 Td
(runtime)Tj
3.4752 0 Td
(and)Tj
-35.5405 -1.3039 Td
(memory)Tj
3.6169 0 Td
(usage.)Tj
2.6532 0 Td
(Hence,)Tj
3.0331 0 Td
(the)Tj
1.4683 0 Td
(range)Tj
2.4662 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
0.6803 0 Td
(values)Tj
2.6702 0 Td
(to)Tj
1.0261 0 Td
(which)Tj
2.6476 0 Td
(they)Tj
1.9275 0 Td
(can)Tj
1.6214 0 Td
(be)Tj
1.1509 0 Td
(applied)Tj
3.1578 0 Td
(is)Tj
0.8447 0 Td
(limited.)Tj
3.2938 0 Td
(To)Tj
1.338 0 Td
(extend)Tj
-34.6108 -1.2982 Td
(this)Tj
1.6724 0 Td
(range,)Tj
2.6872 0 Td
(we)Tj
1.3266 0 Td
(present)Tj
3.1635 0 Td
(below)Tj
2.5908 0 Td
(a)Tj
0.652 0 Td
(procedure)Tj
4.3143 0 Td
(to)Tj
1.0261 0 Td
(construct)Tj
3.9798 0 Td
(a)Tj
0.652 0 Td
(universal)Tj
/F10 1 Tf
3.8551 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6475 0 Td
(hitting)Tj
2.897 0 Td
(set)Tj
1.2983 0 Td
(by)Tj
1.1849 0 Td
(extend-)Tj
-33.9475 -1.2983 Td
(ing)Tj
1.5023 0 Td
(UHSs)Tj
2.5568 0 Td
(computed)Tj
4.2633 0 Td
(for)Tj
1.389 0 Td
(smaller)Tj
/F10 1 Tf
3.1237 0 Td
[()]TJ
/F9 1 Tf
0.6804 0 Td
(values.)Tj
2.8969 0 Td
(Given)Tj
2.6249 0 Td
(a)Tj
0.6576 0 Td
(set)Tj
/F10 1 Tf
1.304 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 416.9196 554.4 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[(,)]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.1565 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 431.7732 556.1007 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(and)Tj
1.7291 0 Td
(integer)Tj
/F10 1 Tf
3.016 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.703 0 Td
(we)Tj
1.3266 0 Td
(can)Tj
1.6271 0 Td
(construct)Tj
3.9798 0 Td
(set)Tj
/F10 1 Tf
-35.5575 -1.3039 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 206.9291 541.4173 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+)Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.8141 0 Td
[()]TJ
/F9 1 Tf
(+)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 232.9511 543.0614 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(by)Tj
1.1848 0 Td
(concatenating)Tj
5.8394 0 Td
(all)Tj
1.1451 0 Td
(possible)Tj
/F10 1 Tf
3.4073 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
2.8063 0 Td
(over)Tj
/F19 1 Tf
1.9729 0 Td
(S)Tj
/F9 1 Tf
0.8844 0 Td
(to)Tj
1.0261 0 Td
(each)Tj
/F10 1 Tf
2.0296 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6475 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 479.7354 541.4173 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
0.9751 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 491.0173 543.0614 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
0.4478 0 Td
(Formally,)Tj
/F10 1 Tf
0 Tc
-18.7028 -1.9275 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 315.4393 521.2913 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F15 1 Tf
()Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
(;)Tj
/F10 1 Tf
[()]TJ
/F15 1 Tf
()Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 338.7401 523.7858 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
1.0488 0 Td
(f)Tj
/F10 1 Tf
[(!)]TJ
/F15 1 Tf
1.3889 0 Td
()Tj
/F10 1 Tf
0.4933 0 Td
[(+)]TJ
/F15 1 Tf
0.771 0 Td
(j)Tj
/F10 1 Tf
0.5442 0 Td
[(!)]TJ
/F15 1 Tf
0.9468 0 Td
(2)Tj
/F10 1 Tf
0.9354 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 406.9984 521.2913 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
/F20 1 Tf
(;)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 415.1622 523.7858 cm
BT
/F20 1 Tf
1 TL
0 0 Td
(;)Tj
/F10 1 Tf
0.4365 0 Td
[(+)]TJ
/F15 1 Tf
0.7653 0 Td
(2)Tj
/F19 1 Tf
0.9355 0 Td
(S)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 443.2251 528.2078 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 445.2661 523.7858 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(g)Tj
11.3441 0 Td
()Tj
/F9 1 Tf
(10)Tj
/F15 1 Tf
()Tj
/F9 1 Tf
-0.005 Tc
-35.8692 -2.3017 Td
(To)Tj
1.3322 0 Td
(see)Tj
1.4287 0 Td
(that)Tj
/F10 1 Tf
1.7745 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 252.2834 499.1244 cm
BT
/F10 1 Tf
1 TL
-0.0067 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+)Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.8141 0 Td
[()]TJ
/F9 1 Tf
(+)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 278.2488 500.7685 cm
BT
/F9 1 Tf
1 TL
-0.005 Tc
0 0 Td
(is)Tj
0.8447 0 Td
(a)Tj
0.6519 0 Td
(universal)Tj
3.8438 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
1.0261 0 Td
(+)Tj
/F10 1 Tf
0.7994 0 Td
[()]TJ
/F9 1 Tf
(\)-mer)Tj
2.7723 0 Td
(hitting)Tj
2.8856 0 Td
(set,)Tj
1.525 0 Td
(denote)Tj
2.9424 0 Td
(by)Tj
/F10 1 Tf
1.1792 0 Td
[( )]TJ
/F9 1 Tf
0.6746 0 Td
(an)Tj
1.2019 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
1.0885 0 Td
(+)Tj
/F10 1 Tf
0.7994 0 Td
[()]TJ
/F9 1 Tf
(\)-long)Tj
2.9253 0 Td
(sequence.)Tj
-32.9836 -1.2982 Td
(By)Tj
1.2415 0 Td
(definition,)Tj
4.371 0 Td
(there)Tj
2.2506 0 Td
(must)Tj
2.211 0 Td
(be)Tj
1.1396 0 Td
(at)Tj
0.9467 0 Td
(least)Tj
1.9673 0 Td
(one)Tj
/F10 1 Tf
1.6894 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
/F10 1 Tf
2.6362 0 Td
[(!)]TJ
/F15 1 Tf
0 Tc
0.8731 0 Td
(2)Tj
/F10 1 Tf
-0.005 Tc
0.8674 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 408.8692 486.085 cm
BT
/F10 1 Tf
1 TL
-0.0067 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
0.9675 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 422.1921 487.7858 cm
BT
/F9 1 Tf
1 TL
-0.005 Tc
0 0 Td
(that)Tj
1.7631 0 Td
(hits)Tj
/F10 1 Tf
1.6667 0 Td
[( )]TJ
/F9 1 Tf
('s)Tj
/F10 1 Tf
1.2359 0 Td
[()]TJ
/F9 1 Tf
(-long)Tj
2.8517 0 Td
(prefix.)Tj
/F10 1 Tf
2.7609 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 531.9496 486.085 cm
BT
/F10 1 Tf
1 TL
-0.0067 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(+)Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.7915 0 Td
[()]TJ
/F9 1 Tf
(+)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 557.6881 487.7858 cm
BT
/F9 1 Tf
1 TL
-0.005 Tc
0 0 Td
(con-)Tj
-35.7673 -1.3039 Td
(tains)Tj
2.1203 0 Td
(all)Tj
1.1452 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
1.0261 0 Td
(+)Tj
/F10 1 Tf
0.7994 0 Td
[()]TJ
/F9 1 Tf
(\)-mers)Tj
/F10 1 Tf
3.1351 0 Td
[(!)]TJ
/F15 1 Tf
0 Tc
0.8787 0 Td
()Tj
/F10 1 Tf
-0.005 Tc
0.4933 0 Td
[(+)]TJ
/F9 1 Tf
(,)Tj
0.907 0 Td
(where)Tj
/F10 1 Tf
2.6476 0 Td
[(+)]TJ
/F9 1 Tf
0.6803 0 Td
(is)Tj
0.8504 0 Td
(any)Tj
/F10 1 Tf
1.6497 0 Td
[()]TJ
/F9 1 Tf
(-mer.)Tj
2.6646 0 Td
(Thus,)Tj
2.4661 0 Td
(it)Tj
0.7824 0 Td
(must)Tj
2.2223 0 Td
(contain)Tj
3.2428 0 Td
(a)Tj
0.652 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
1.0261 0 Td
(+)Tj
/F10 1 Tf
0.7994 0 Td
[()]TJ
/F9 1 Tf
(\)-mer)Tj
2.7723 0 Td
(that)Tj
1.7744 0 Td
(hits)Tj
/F10 1 Tf
1.6724 0 Td
[( )]TJ
/F9 1 Tf
(.)Tj
-0.004 Tc
-35.2117 -1.2982 Td
(For)Tj
1.6271 0 Td
(example,)Tj
3.7757 0 Td
(by)Tj
1.1849 0 Td
(appending)Tj
4.4674 0 Td
(all)Tj
1.1452 0 Td
(possible)Tj
3.4129 0 Td
(10-mers)Tj
3.4922 0 Td
(to)Tj
1.0262 0 Td
(each)Tj
2.0295 0 Td
(10-mer)Tj
3.1351 0 Td
(in)Tj
/F10 1 Tf
1.0375 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 482.2299 460.1196 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(10,20)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 500.3716 461.7637 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(we)Tj
1.3266 0 Td
(obtain)Tj
/F10 1 Tf
2.7836 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 548.3905 460.1196 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(20,30)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 564.3212 461.7637 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(.)Tj
-36.4306 -1.4626 Td
(The)Tj
1.7802 0 Td
(size)Tj
1.6837 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.474 0 Td
(set)Tj
/F10 1 Tf
1.2983 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 279.496 445.4362 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(10,20)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 297.5811 447.137 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8503 0 Td
(|)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 315.6094 445.4362 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(10,20)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 331.4834 447.137 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(|)Tj
0.4762 0 Td
(=)Tj
/F10 1 Tf
0.7993 0 Td
[( )]TJ
/F15 1 Tf
0 Tc
0.5953 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.4876 0 Td
[()4()7( )]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 367.7102 445.4362 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(10)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 374.7968 447.137 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4478 0 Td
(where)Tj
/F10 1 Tf
0 Tc
2.6476 0 Td
[()4()7( )]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 418.3937 444.6425 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(10)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 427.6346 447.137 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
438.1228 449.8016 m
446.6268 449.8016 l
446.6268 449.4047 l
438.1228 449.4047 l
f*
5.9998 0 0 5.9998 438.1228 450.7653 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(4)Tj
ET
Q
q
1 j
1 J
0 w
5 0 0 5 441.1275 452.9196 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(10)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 439.37 443.7354 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(10)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 448.7811 447.137 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
0.8503 0 Td
(the)Tj
1.4684 0 Td
(size)Tj
1.6837 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
0.6577 0 Td
(minimum)Tj
4.2859 0 Td
(decy-)Tj
-34.8374 -1.4059 Td
(cling)Tj
2.1713 0 Td
(set)Tj
1.2982 0 Td
(for)Tj
/F10 1 Tf
1.389 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(=)Tj
0.7994 0 Td
(10)Tj
1.1735 0 Td
(\()Tj
0.83 0.64 0.02 0 k
(Eq)Tj
1.6327 0 Td
(11)Tj
0 g
(\).)Tj
1.7348 0 Td
(Here)Tj
/F10 1 Tf
2.211 0 Td
[( )]TJ
/F15 1 Tf
0 Tc
0.5896 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9922 0 Td
(1)Tj
0.6916 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4683 0 Td
(approximation)Tj
6.1739 0 Td
(factor)Tj
2.5453 0 Td
(obtained)Tj
3.7304 0 Td
(by)Tj
1.1849 0 Td
(the)Tj
1.4683 0 Td
(UHS.)Tj
2.4208 0 Td
(Then,)Tj
-35.2116 -1.4627 Td
(the)Tj
1.4683 0 Td
(size)Tj
1.6838 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 248.5984 416.7496 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(20,30)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 266.7401 418.4503 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(is)Tj
/F15 1 Tf
0 Tc
0.8447 0 Td
(j)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 284.8818 415.9559 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(20)Tj
/F20 1 Tf
(;)Tj
/F18 1 Tf
(30)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 298.9417 418.4503 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(j)Tj
0.5442 0 Td
()Tj
1.0488 0 Td
(j)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 324.5669 415.9559 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(10)Tj
/F20 1 Tf
(;)Tj
/F18 1 Tf
(20)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 338.6267 418.4503 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(j)Tj
0.4932 0 Td
()Tj
/F18 1 Tf
0.4932 0 Td
(4)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 353.4803 422.8724 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(10)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 362.7212 418.4503 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F10 1 Tf
1.0488 0 Td
[( )]TJ
/F15 1 Tf
0.5952 0 Td
()Tj
/F10 1 Tf
0.4933 0 Td
[()4()7( )]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 396.737 415.9559 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(10)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 405.4677 418.4503 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F18 1 Tf
0.4932 0 Td
(4)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 415.3889 422.8724 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(10)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 424.6299 418.4503 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F10 1 Tf
1.0488 0 Td
[( )]TJ
/F15 1 Tf
0.5952 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
446.0031 421.115 m
454.5071 421.115 l
454.5071 420.7181 l
446.0031 420.7181 l
f*
5.9998 0 0 5.9998 446.0031 422.0787 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(4)Tj
ET
Q
q
1 j
1 J
0 w
5 0 0 5 449.0078 424.233 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(20)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 447.2503 415.0488 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(10)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 457.285 418.4503 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F18 1 Tf
1.0488 0 Td
(2)Tj
/F10 1 Tf
[( )]TJ
/F15 1 Tf
1.0998 0 Td
()Tj
ET
Q
q
1 j
1 J
0 w
483.7039 421.115 m
492.1512 421.115 l
492.1512 420.7181 l
483.7039 420.7181 l
f*
5.9998 0 0 5.9998 483.7039 422.0787 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(4)Tj
ET
Q
q
1 j
1 J
0 w
5 0 0 5 486.7086 424.233 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(20)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 484.9511 415.0488 cm
BT
/F18 1 Tf
1 TL
0 0 Td
(20)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 494.3622 418.4503 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(by)Tj
1.1792 0 Td
(this)Tj
1.6724 0 Td
(construction.)Tj
-32.2863 -1.4116 Td
(This)Tj
1.9842 0 Td
(is)Tj
0.8504 0 Td
(approximately)Tj
5.9754 0 Td
(|)Tj
/F10 1 Tf
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 297.6377 402.633 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(20,30)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 313.5118 404.3338 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(|)Tj
/F15 1 Tf
0 Tc
0.4762 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9921 0 Td
(2)Tj
/F10 1 Tf
[( )]TJ
/F15 1 Tf
0 Tc
1.0658 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.4932 0 Td
[()4()7( )]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 356.3716 402.633 cm
BT
/F9 1 Tf
1 TL
-0.0053 Tc
0 0 Td
(20)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 363.5149 404.3338 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4422 0 Td
(i.e.)Tj
1.3662 0 Td
(the)Tj
1.4684 0 Td
(approximation)Tj
6.1738 0 Td
(factor)Tj
2.5398 0 Td
(doubled.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 374.0031 cm
BT
/F3 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(Results)Tj
/F0 1 Tf
0 -1.5023 Td
(A)Tj
0.8834 0 Td
(theoretical)Tj
4.7717 0 Td
(lower)Tj
2.5748 0 Td
(bound)Tj
2.9623 0 Td
(for)Tj
1.3748 0 Td
(|)Tj
/F7 1 Tf
(U)Tj
ET
Q
q
1 j
1 J
0 w
8.9997 0 0 7.999 362.4944 353.9905 cm
BT
/F7 1 Tf
1 TL
-0.0044 Tc
0 0 Td
(k)Tj
/F0 1 Tf
(,)Tj
/F7 1 Tf
1.0646 0 Td
(L)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 377.0078 355.9748 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(|)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 338.9669 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(For)Tj
1.627 0 Td
(a)Tj
0.652 0 Td
(given)Tj
/F10 1 Tf
2.3811 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
/F10 1 Tf
2.6475 0 Td
[(!)]TJ
/F9 1 Tf
(,)Tj
1.1112 0 Td
(its)Tj
/F10 1 Tf
1.1452 0 Td
[( )7()11()18()14(\r)10()2()6( )-9($)]TJ
4.0705 0 Td
[( )13()4(\n)10(\n)]TJ
/F9 1 Tf
1.9729 0 Td
(is)Tj
0.8504 0 Td
(the)Tj
1.4683 0 Td
(set)Tj
1.304 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0103 0 Td
(obtained)Tj
3.7304 0 Td
(by)Tj
1.1849 0 Td
(rotation)Tj
3.4526 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[(!)]TJ
/F9 1 Tf
(.)Tj
1.1055 0 Td
(Conju-)Tj
-33.7434 -1.2982 Td
(gacy)Tj
1.9955 0 Td
(classes)Tj
2.829 0 Td
(form)Tj
2.2053 0 Td
(cycles)Tj
2.5569 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.4683 0 Td
(de)Tj
1.1735 0 Td
(Bruijn)Tj
2.7723 0 Td
(graph)Tj
2.5342 0 Td
(and)Tj
1.7291 0 Td
(form)Tj
2.2053 0 Td
(a)Tj
0.6577 0 Td
(partition)Tj
3.7303 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
/F10 1 Tf
1.4684 0 Td
[()]TJ
/F9 1 Tf
(-mers.)Tj
3.2371 0 Td
(The)Tj
1.7802 0 Td
(number)Tj
-34.3897 -1.2983 Td
(of)Tj
1.0147 0 Td
(conjugacy)Tj
4.2577 0 Td
(classes)Tj
2.8346 0 Td
(over)Tj
1.9729 0 Td
(all)Tj
/F10 1 Tf
1.1452 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.016 0 Td
(is)Tj
0.8447 0 Td
(given)Tj
2.3811 0 Td
(by)Tj
1.1792 0 Td
([)Tj
0.83 0.64 0.02 0 k
(16)Tj
0 g
(]:)Tj
/F10 1 Tf
0 Tc
-6.582 -2.7722 Td
[(-)]TJ
/F15 1 Tf
0.6577 0 Td
(j)Tj
/F19 1 Tf
(S)Tj
/F15 1 Tf
(j)Tj
/F20 1 Tf
(;)Tj
/F10 1 Tf
2.0352 0 Td
[()]TJ
/F15 1 Tf
()Tj
1.1282 0 Td
()Tj
/F21 1 Tf
1.0488 0.9467 Td
(X)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 375.137 296.7307 cm
BT
/F10 1 Tf
1 TL
0 0 Td
[()]TJ
-0.5385 -3.6568 Td
[()]TJ
/F15 1 Tf
()Tj
/F18 1 Tf
(1)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 385.3417 285.2787 cm
BT
/F15 1 Tf
1 TL
0 0 Td
(j)Tj
/F19 1 Tf
(S)Tj
/F15 1 Tf
(j)Tj
/F17 1 Tf
1.3662 0.5159 Td
[()7()-1()]TJ
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.9998 414.4251 290.4377 cm
BT
/F15 1 Tf
1 TL
0 0 Td
()Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
(;)Tj
/F10 1 Tf
[()]TJ
/F15 1 Tf
()Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 425.6503 285.2787 cm
BT
/F20 1 Tf
1 TL
0 0 Td
(=)Tj
/F10 1 Tf
[()]TJ
/F20 1 Tf
(:)Tj
/F15 1 Tf
13.3057 0 Td
()Tj
/F9 1 Tf
(11)Tj
/F15 1 Tf
()Tj
/F9 1 Tf
-0.004 Tc
-34.6731 -3.1521 Td
(A)Tj
0.9071 0 Td
(decycling)Tj
4.0025 0 Td
(set)Tj
1.2983 0 Td
(necessarily)Tj
4.5354 0 Td
(contains)Tj
3.6113 0 Td
(a)Tj
/F10 1 Tf
0.6519 0 Td
[()]TJ
/F9 1 Tf
(-mer)Tj
2.6476 0 Td
(from)Tj
2.2053 0 Td
(each)Tj
2.0295 0 Td
(conjugacy)Tj
4.2633 0 Td
(class.)Tj
2.2677 0 Td
(Golomb's)Tj
4.0989 0 Td
(conjec-)Tj
-33.715 -1.2982 Td
(ture,)Tj
2.0636 0 Td
(proved)Tj
3.0217 0 Td
(by)Tj
1.1849 0 Td
(Mykkeltveit)Tj
4.9719 0 Td
([)Tj
0.83 0.64 0.02 0 k
(17)Tj
0 g
(],)Tj
2.075 0 Td
(states)Tj
2.3981 0 Td
(that)Tj
1.7745 0 Td
(the)Tj
1.474 0 Td
(smallest)Tj
3.4072 0 Td
(decycling)Tj
4.0024 0 Td
(set)Tj
1.2982 0 Td
(has)Tj
1.5478 0 Td
(cardinality)Tj
/F10 1 Tf
4.49 0 Td
[(-)]TJ
/F9 1 Tf
(\(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|,)Tj
/F10 1 Tf
2.5852 0 Td
[()]TJ
/F9 1 Tf
(\).)Tj
-36.2945 -1.3039 Td
(Consequently,)Tj
5.9527 0 Td
(a)Tj
0.652 0 Td
(minimum)Tj
4.2916 0 Td
(hitting)Tj
2.8913 0 Td
(set)Tj
/F10 1 Tf
1.304 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 357.9023 226.0913 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
0.9751 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 371.3952 227.7354 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(has)Tj
1.542 0 Td
(a)Tj
0.652 0 Td
(size)Tj
/F15 1 Tf
0 Tc
1.6837 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[(-)]TJ
/F9 1 Tf
(\(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|,)Tj
/F10 1 Tf
2.5852 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
/F15 1 Tf
0 Tc
1.0262 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9921 0 Td
(|)Tj
/F19 1 Tf
(S)Tj
/F9 1 Tf
(|)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 477.8645 232.2141 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 481.3795 227.7354 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(/)Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(.)Tj
0.83 0.64 0.02 0 k
-26.9403 -1.2982 Td
(Table)Tj
2.4435 0 Td
(1)Tj
0 g
0.6973 0 Td
(reports)Tj
/F10 1 Tf
3.0671 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 279.3259 213.1086 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()6(+)]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 292.3086 214.7527 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(,)Tj
0.4422 0 Td
(the)Tj
1.4683 0 Td
(length)Tj
2.7326 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(longest)Tj
3.0727 0 Td
(sequence)Tj
3.8551 0 Td
(in)Tj
1.0375 0 Td
(a)Tj
0.652 0 Td
(complete)Tj
3.8777 0 Td
(de)Tj
1.1736 0 Td
(Bruijn)Tj
2.7722 0 Td
(graph)Tj
2.5342 0 Td
(after)Tj
-35.3307 -1.2982 Td
(a)Tj
0.652 0 Td
(minimum)Tj
4.2916 0 Td
(decycling)Tj
3.9968 0 Td
(set)Tj
1.3038 0 Td
(computed)Tj
4.2633 0 Td
(using)Tj
2.3925 0 Td
(Mykkeltveit's)Tj
5.5502 0 Td
(algorithm)Tj
4.1555 0 Td
(is)Tj
0.8447 0 Td
(removed,)Tj
3.9742 0 Td
(for)Tj
/F10 1 Tf
1.389 0 Td
[()]TJ
/F9 1 Tf
0.6803 0 Td
(=)Tj
0.7993 0 Td
(2)Tj
0.6973 0 Td
(to)Tj
1.0262 0 Td
(14.)Tj
-36.0167 -1.3039 Td
(For)Tj
1.6271 0 Td
(this)Tj
1.6724 0 Td
(range)Tj
2.4605 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9127 0 Td
(the)Tj
1.4683 0 Td
(length)Tj
2.7325 0 Td
(of)Tj
1.0148 0 Td
(sequences)Tj
4.218 0 Td
(avoiding)Tj
3.6906 0 Td
(the)Tj
1.4684 0 Td
(decycling)Tj
4.0025 0 Td
(set)Tj
1.3039 0 Td
(can)Tj
1.6214 0 Td
(theoretically)Tj
5.142 0 Td
(be)Tj
-34.3499 -1.2983 Td
(appropriate)Tj
4.8756 0 Td
(for)Tj
1.3889 0 Td
(long-read)Tj
4.0931 0 Td
(sequencing)Tj
4.7169 0 Td
(technologies,)Tj
5.4424 0 Td
(such)Tj
2.058 0 Td
(as)Tj
1.0148 0 Td
(PacBio)Tj
2.9933 0 Td
([)Tj
0.83 0.64 0.02 0 k
(19)Tj
0 g
(])Tj
1.8482 0 Td
(and)Tj
1.7348 0 Td
(Nanopore)Tj
4.2633 0 Td
([)Tj
0.83 0.64 0.02 0 k
(20)Tj
0 g
(],)Tj
-34.4293 -1.2983 Td
(which)Tj
2.6475 0 Td
(produce)Tj
3.5207 0 Td
(reads)Tj
2.3357 0 Td
(of)Tj
1.0147 0 Td
(length)Tj
/F10 1 Tf
2.7326 0 Td
[()]TJ
/F20 1 Tf
0 Tc
0.7426 0 Td
(>)Tj
/F9 1 Tf
-0.004 Tc
0.9922 0 Td
(1000.)Tj
2.3527 0 Td
(Such)Tj
2.1713 0 Td
(long)Tj
1.9899 0 Td
(reads)Tj
2.3358 0 Td
(are)Tj
1.4456 0 Td
(all)Tj
1.1509 0 Td
(hit)Tj
1.3096 0 Td
(by)Tj
1.1849 0 Td
(a)Tj
0.6519 0 Td
(decycling)Tj
4.0025 0 Td
(set)Tj
ET
Q
q
0.45 0.36 0.35 0.01 k
1 j
1 J
0 w
36 125.1371 m
576 125.1371 l
576 124.6371 l
36 124.6371 l
f*
76.0266 124.6371 m
76.0266 112.1372 l
75.5266 112.1372 l
75.5266 124.6371 l
f*
75.5266 112.1372 m
36 112.1372 l
36 112.6372 l
75.5266 112.6372 l
f*
107.7508 124.6371 m
107.7508 112.1372 l
107.2508 112.1372 l
107.2508 124.6371 l
f*
107.2508 112.1372 m
76.0266 112.1372 l
76.0266 112.6372 l
107.2508 112.6372 l
f*
143.8778 124.6371 m
143.8778 112.1372 l
143.3778 112.1372 l
143.3778 124.6371 l
f*
143.3778 112.1372 m
107.7508 112.1372 l
107.7508 112.6372 l
143.3778 112.6372 l
f*
180.0048 124.6371 m
180.0048 112.1372 l
179.5048 112.1372 l
179.5048 124.6371 l
f*
179.5048 112.1372 m
143.8778 112.1372 l
143.8778 112.6372 l
179.5048 112.6372 l
f*
216.1318 124.6371 m
216.1318 112.1372 l
215.6318 112.1372 l
215.6318 124.6371 l
f*
215.6318 112.1372 m
180.0048 112.1372 l
180.0048 112.6372 l
215.6318 112.6372 l
f*
252.2588 124.6371 m
252.2588 112.1372 l
251.7588 112.1372 l
251.7588 124.6371 l
f*
251.7588 112.1372 m
216.1318 112.1372 l
216.1318 112.6372 l
251.7588 112.6372 l
f*
292.7886 124.6371 m
292.7886 112.1372 l
292.2885 112.1372 l
292.2885 124.6371 l
f*
292.2885 112.1372 m
252.2588 112.1372 l
252.2588 112.6372 l
292.2885 112.6372 l
f*
333.3183 124.6371 m
333.3183 112.1372 l
332.8183 112.1372 l
332.8183 124.6371 l
f*
332.8183 112.1372 m
292.7886 112.1372 l
292.7886 112.6372 l
332.8183 112.6372 l
f*
373.8481 124.6371 m
373.8481 112.1372 l
373.3481 112.1372 l
373.3481 124.6371 l
f*
373.3481 112.1372 m
333.3183 112.1372 l
333.3183 112.6372 l
373.3481 112.6372 l
f*
414.3779 124.6371 m
414.3779 112.1372 l
413.8778 112.1372 l
413.8778 124.6371 l
f*
413.8778 112.1372 m
373.8481 112.1372 l
373.8481 112.6372 l
413.8778 112.6372 l
f*
454.9076 124.6371 m
454.9076 112.1372 l
454.4076 112.1372 l
454.4076 124.6371 l
f*
454.4076 112.1372 m
414.3779 112.1372 l
414.3779 112.6372 l
454.4076 112.6372 l
f*
495.4374 124.6371 m
495.4374 112.1372 l
494.9374 112.1372 l
494.9374 124.6371 l
f*
494.9374 112.1372 m
454.9076 112.1372 l
454.9076 112.6372 l
494.9374 112.6372 l
f*
535.9671 124.6371 m
535.9671 112.1372 l
535.4671 112.1372 l
535.4671 124.6371 l
f*
535.4671 112.1372 m
495.4374 112.1372 l
495.4374 112.6372 l
535.4671 112.6372 l
f*
575.9969 112.1372 m
535.9671 112.1372 l
535.9671 112.6372 l
575.9969 112.6372 l
f*
76.0266 112.1372 m
76.0266 99.6372 l
75.5266 99.6372 l
75.5266 112.1372 l
f*
75.5266 99.6372 m
36 99.6372 l
36 100.1373 l
75.5266 100.1373 l
f*
107.7508 112.1372 m
107.7508 99.6372 l
107.2508 99.6372 l
107.2508 112.1372 l
f*
107.2508 99.6372 m
76.0266 99.6372 l
76.0266 100.1373 l
107.2508 100.1373 l
f*
143.8778 112.1372 m
143.8778 99.6372 l
143.3778 99.6372 l
143.3778 112.1372 l
f*
143.3778 99.6372 m
107.7508 99.6372 l
107.7508 100.1373 l
143.3778 100.1373 l
f*
180.0048 112.1372 m
180.0048 99.6372 l
179.5048 99.6372 l
179.5048 112.1372 l
f*
179.5048 99.6372 m
143.8778 99.6372 l
143.8778 100.1373 l
179.5048 100.1373 l
f*
216.1318 112.1372 m
216.1318 99.6372 l
215.6318 99.6372 l
215.6318 112.1372 l
f*
215.6318 99.6372 m
180.0048 99.6372 l
180.0048 100.1373 l
215.6318 100.1373 l
f*
252.2588 112.1372 m
252.2588 99.6372 l
251.7588 99.6372 l
251.7588 112.1372 l
f*
251.7588 99.6372 m
216.1318 99.6372 l
216.1318 100.1373 l
251.7588 100.1373 l
f*
292.7886 112.1372 m
292.7886 99.6372 l
292.2885 99.6372 l
292.2885 112.1372 l
f*
292.2885 99.6372 m
252.2588 99.6372 l
252.2588 100.1373 l
292.2885 100.1373 l
f*
333.3183 112.1372 m
333.3183 99.6372 l
332.8183 99.6372 l
332.8183 112.1372 l
f*
332.8183 99.6372 m
292.7886 99.6372 l
292.7886 100.1373 l
332.8183 100.1373 l
f*
373.8481 112.1372 m
373.8481 99.6372 l
373.3481 99.6372 l
373.3481 112.1372 l
f*
373.3481 99.6372 m
333.3183 99.6372 l
333.3183 100.1373 l
373.3481 100.1373 l
f*
414.3779 112.1372 m
414.3779 99.6372 l
413.8778 99.6372 l
413.8778 112.1372 l
f*
413.8778 99.6372 m
373.8481 99.6372 l
373.8481 100.1373 l
413.8778 100.1373 l
f*
454.9076 112.1372 m
454.9076 99.6372 l
454.4076 99.6372 l
454.4076 112.1372 l
f*
454.4076 99.6372 m
414.3779 99.6372 l
414.3779 100.1373 l
454.4076 100.1373 l
f*
495.4374 112.1372 m
495.4374 99.6372 l
494.9374 99.6372 l
494.9374 112.1372 l
f*
494.9374 99.6372 m
454.9076 99.6372 l
454.9076 100.1373 l
494.9374 100.1373 l
f*
535.9671 112.1372 m
535.9671 99.6372 l
535.4671 99.6372 l
535.4671 112.1372 l
f*
535.4671 99.6372 m
495.4374 99.6372 l
495.4374 100.1373 l
535.4671 100.1373 l
f*
575.9969 99.6372 m
535.9671 99.6372 l
535.9671 100.1373 l
575.9969 100.1373 l
f*
0.83 0.64 0.02 0 k
36 86.5701 m
184.5354 86.5701 l
h
f*
0 g
7.9999 0 0 7.9999 36 139.4645 cm
BT
/F3 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Table)Tj
2.7992 0 Td
(1.)Tj
1.0417 0 Td
(Length)Tj
3.5221 0 Td
(of)Tj
1.1551 0 Td
(longest)Tj
3.7418 0 Td
(sequence)Tj
4.7693 0 Td
(avoidin)Tj
3.4583 0 Td
(g)Tj
0.8292 0 Td
(an)Tj
1.3748 0 Td
(unavoidab)Tj
4.9465 0 Td
(le)Tj
1.0417 0 Td
(set)Tj
1.637 0 Td
(for)Tj
1.5378 0 Td
(different)Tj
4.1599 0 Td
(values)Tj
3.2882 0 Td
(of)Tj
/F23 1 Tf
1.1551 0 Td
(k)Tj
/F3 1 Tf
(.)Tj
/F0 1 Tf
1.0347 0 Td
(For)Tj
1.7008 0 Td
(each)Tj
2.3528 0 Td
(value)Tj
/F7 1 Tf
2.5654 0 Td
(k)Tj
/F0 1 Tf
(,)Tj
0.985 0 Td
(a)Tj
0.7654 0 Td
(minimum)Tj
4.2165 0 Td
(decycling)Tj
4.3087 0 Td
(set)Tj
1.5307 0 Td
(was)Tj
1.9701 0 Td
(removed)Tj
-61.8878 -1.1905 Td
(from)Tj
2.1968 0 Td
(a)Tj
0.7654 0 Td
(complet)Tj
3.437 0 Td
(e)Tj
0.7654 0 Td
(de)Tj
1.311 0 Td
(Bruijn)Tj
2.7284 0 Td
(graph,)Tj
3.0047 0 Td
(and)Tj
1.8567 0 Td
(the)Tj
1.5804 0 Td
(length)Tj
/F7 1 Tf
2.8913 0 Td
(L)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.3325 204.6614 128.6362 cm
BT
/F7 1 Tf
1 TL
-0.0067 Tc
0 0 Td
(max)Tj
ET
Q
q
1 j
1 J
0 w
7.9999 0 0 7.9999 217.5874 129.9401 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(of)Tj
1.0417 0 Td
(the)Tj
1.5874 0 Td
(longest)Tj
3.3803 0 Td
(sequence,)Tj
4.7552 0 Td
(represented)Tj
5.4638 0 Td
(as)Tj
1.2615 0 Td
(a)Tj
0.7653 0 Td
(longest)Tj
3.3804 0 Td
(path,)Tj
2.4094 0 Td
(was)Tj
1.9701 0 Td
(calculated)Tj
4.415 0 Td
(.)Tj
/F7 1 Tf
0 Tc
-51.0948 -1.8496 Td
(k)Tj
/F0 1 Tf
4.6489 0 Td
(2)Tj
4.2378 0 Td
(3)Tj
4.5142 0 Td
(4)Tj
4.5142 0 Td
(5)Tj
4.5212 0 Td
(6)Tj
4.7906 0 Td
(7)Tj
5.067 0 Td
(8)Tj
5.0669 0 Td
(9)Tj
4.7906 0 Td
(10)Tj
5.067 0 Td
(11)Tj
5.0599 0 Td
(12)Tj
5.067 0 Td
(13)Tj
5.0669 0 Td
(14)Tj
/F7 1 Tf
-63.1421 -1.5661 Td
(L)Tj
ET
Q
q
1 j
1 J
0 w
5.9998 0 0 5.3325 50.7968 101.3102 cm
BT
/F7 1 Tf
1 TL
0 0 Td
(max)Tj
ET
Q
q
1 j
1 J
0 w
7.9999 0 0 7.9999 89.4614 102.6141 cm
BT
/F0 1 Tf
1 TL
0 0 Td
(5)Tj
3.9614 0 Td
(11)Tj
4.5142 0 Td
(20)Tj
4.5213 0 Td
(45)Tj
4.5142 0 Td
(70)Tj
4.5142 0 Td
(117)Tj
5.067 0 Td
(148)Tj
5.067 0 Td
(239)Tj
5.0669 0 Td
(311)Tj
5.067 0 Td
(413)Tj
5.067 0 Td
(570)Tj
5.0669 0 Td
(697)Tj
5.0599 0 Td
(931)Tj
0.83 0.64 0.02 0 k
/F12 1 Tf
-0.025 Tc
-64.1697 -1.8708 Td
(https://do)Tj
3.5575 0 Td
(i.org/10.1371/j)Tj
5.4425 0 Td
(ournal.pc)Tj
3.4583 0 Td
(bi.1005777.)Tj
4.4292 0 Td
(t001)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 169.285 23.6976 re
W* n
q
169.2283 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 450.4818 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Compact)Tj
4.1669 0 Td
(universal)Tj
/F7 1 Tf
4.1386 0 Td
(k)Tj
/F0 1 Tf
(-mer)Tj
2.7355 0 Td
(hitting)Tj
2.8346 0 Td
(sets)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
142.5827 34.9228 m
295.8236 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(Computationa)Tj
6.1229 0 Td
(l)Tj
0.4322 0 Td
(Biology)Tj
3.4371 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https:/)Tj
2.6788 0 Td
(/doi.org/10.13)Tj
6.0094 0 Td
(71/journal.p)Tj
5.1166 0 Td
(cbi.1005777)Tj
0 g
6.3497 0 Td
(October)Tj
3.7276 0 Td
(2,)Tj
1.0346 0 Td
(2017)Tj
26.901 0 Td
(8)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
150 0 obj
<>stream
endstream
endobj
151 0 obj
<>stream
endstream
endobj
152 0 obj
<>stream
endstream
endobj
153 0 obj
<>stream
endstream
endobj
154 0 obj
<>stream
endstream
endobj
155 0 obj
<>stream
endstream
endobj
156 0 obj
<>stream
endstream
endobj
157 0 obj
<>stream
endstream
endobj
158 0 obj
<>stream
endstream
endobj
159 0 obj
<>stream
endstream
endobj
160 0 obj
<>stream
endstream
endobj
161 0 obj
<>stream
endstream
endobj
162 0 obj
<>stream
BT
66.402 0 Td
(15)Tj
ET
Q
endstream
endobj
163 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 17 0 R/Annots 164 0 R/Contents 165 0 R/TrimBox[0 0 612 792]>>
endobj
164 0 obj
[166 0 R 167 0 R 168 0 R 169 0 R 170 0 R 171 0 R 172 0 R 173 0 R 174 0 R 175 0 R 176 0 R 177 0 R 178 0 R 179 0 R 180 0 R 181 0 R 182 0 R]
endobj
166 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.t001)>>
endobj
167 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref016)>>
endobj
168 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref008)>>
endobj
169 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.ref012)>>
endobj
170 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.g001)>>
endobj
171 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.g001)>>
endobj
172 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.s002)>>
endobj
173 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.g002)>>
endobj
174 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.s001)>>
endobj
175 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.s002)>>
endobj
176 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.s002)>>
endobj
177 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.s001)>>
endobj
178 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.s002)>>
endobj
179 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.s001)>>
endobj
180 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.s001)>>
endobj
181 0 obj
<>/Border[0 0 0]/Dest(Rpcbi.1005777.g002)>>
endobj
182 0 obj
<>/Border[0 0 0]/A 183 0 R>>
endobj
183 0 obj
<>
endobj
165 0 obj
[184 0 R 185 0 R 186 0 R 187 0 R 188 0 R 189 0 R 190 0 R 191 0 R 192 0 R 193 0 R 194 0 R 195 0 R]
endobj
184 0 obj
<>stream
q
0.83 0.64 0.02 0 k
252.1134 706.337 m
281.3669 706.337 l
h
f*
443.3953 641.3102 m
452.9197 641.3102 l
h
f*
466.8661 571.8614 m
471.6283 571.8614 l
h
f*
529.6252 571.8614 m
539.1496 571.8614 l
h
f*
334.6016 532.8567 m
354.1606 532.8567 l
h
f*
211.9748 441.8646 m
238.4504 441.8646 l
h
f*
287.0362 363.8551 m
316.7433 363.8551 l
h
f*
555.3071 294.4063 m
574.8661 294.4063 l
h
f*
300.189 281.3669 m
334.2047 281.3669 l
h
f*
438.5764 281.3669 m
468.2835 281.3669 l
h
f*
286.8094 268.3843 m
316.5165 268.3843 l
h
f*
498.5575 203.4142 m
532.4598 203.4142 l
h
f*
238.1102 120.926 m
267.8173 120.926 l
h
f*
537.9591 94.9039 m
547.4835 94.9039 l
h
f*
200.0126 81.9213 m
222.2362 81.9213 l
h
f*
230.0598 81.9213 m
249.6756 81.9213 l
h
f*
0 g
1 j
1 J
0 w
10 0 0 10 200.0125 707.4141 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(according)Tj
4.1839 0 Td
(to)Tj
0.83 0.64 0.02 0 k
1.0261 0 Td
(Table)Tj
2.4434 0 Td
(1)Tj
0 g
0.6974 0 Td
(for)Tj
/F10 1 Tf
1.3833 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.6859 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9922 0 Td
(14)Tj
1.1735 0 Td
(\(although)Tj
4.0932 0 Td
(a)Tj
0.652 0 Td
(shorter)Tj
3.0784 0 Td
(window)Tj
3.4412 0 Td
(size)Tj
1.6838 0 Td
(may)Tj
1.9275 0 Td
(be)Tj
1.1509 0 Td
(needed)Tj
3.0954 0 Td
(to)Tj
1.0261 0 Td
(overcome)Tj
-32.7342 -1.3039 Td
(sequencing)Tj
4.7168 0 Td
(errors\).)Tj
3.1861 0 Td
(However,)Tj
4.0819 0 Td
(many)Tj
2.4718 0 Td
(short)Tj
2.2903 0 Td
(reads)Tj
2.3358 0 Td
(can)Tj
1.627 0 Td
(avoid)Tj
2.4095 0 Td
(the)Tj
1.4683 0 Td
(decycling)Tj
4.0025 0 Td
(set.)Tj
1.525 0 Td
(Additional)Tj
/F10 1 Tf
4.5298 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
-34.6448 -1.2982 Td
(must)Tj
2.228 0 Td
(be)Tj
1.1452 0 Td
(selected)Tj
3.3505 0 Td
(to)Tj
1.0261 0 Td
(obtain)Tj
2.778 0 Td
(a)Tj
0.6576 0 Td
(hitting)Tj
2.8913 0 Td
(set)Tj
1.3039 0 Td
(for)Tj
1.3833 0 Td
(shorter)Tj
3.0841 0 Td
(sequences.)Tj
4.4447 0 Td
(Note)Tj
2.1827 0 Td
(that)Tj
1.7801 0 Td
(different)Tj
3.6567 0 Td
(minimum)Tj
-31.9122 -1.2983 Td
(decycling)Tj
3.9968 0 Td
(sets)Tj
1.6667 0 Td
(may)Tj
1.9276 0 Td
(result)Tj
2.4491 0 Td
(in)Tj
1.0318 0 Td
(different)Tj
3.6567 0 Td
(lengths)Tj
3.0954 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(longest)Tj
3.0671 0 Td
(path)Tj
2.0012 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
1.4684 0 Td
(remaining)Tj
4.3653 0 Td
(DAG.)Tj
2.5852 0 Td
(Myk-)Tj
-34.8262 -1.2983 Td
(keltveit's)Tj
3.702 0 Td
(approach)Tj
3.9514 0 Td
(is)Tj
0.8504 0 Td
(different)Tj
3.6567 0 Td
(from)Tj
2.2053 0 Td
(that)Tj
1.7802 0 Td
(of)Tj
1.0148 0 Td
(Champarnaud)Tj
6.0207 0 Td
(et)Tj
0.9411 0 Td
(al.)Tj
1.1282 0 Td
(\(2004\),)Tj
3.0274 0 Td
(and)Tj
1.7291 0 Td
(the)Tj
1.474 0 Td
(former)Tj
2.9991 0 Td
(has)Tj
1.542 0 Td
(an)Tj
-36.0224 -1.3039 Td
(advantage)Tj
4.2406 0 Td
(in)Tj
1.0318 0 Td
(producing)Tj
4.3766 0 Td
(solutions)Tj
3.8438 0 Td
(with)Tj
1.9956 0 Td
(shorter)Tj
3.084 0 Td
(longest)Tj
3.0671 0 Td
(paths)Tj
2.3584 0 Td
([)Tj
0.83 0.64 0.02 0 k
(16)Tj
0 g
(].)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 615.9118 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(DOCKS)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 598.9606 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(We)Tj
1.61 0 Td
(implemented)Tj
5.5332 0 Td
(and)Tj
1.7291 0 Td
(ran)Tj
1.5761 0 Td
(DOCKS)Tj
3.5149 0 Td
(over)Tj
1.9786 0 Td
(a)Tj
0.652 0 Td
(range)Tj
2.4604 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(and)Tj
/F10 1 Tf
1.7291 0 Td
[()]TJ
/F9 1 Tf
(:)Tj
0.9751 0 Td
(5)Tj
/F15 1 Tf
0 Tc
0.6973 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9922 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.6803 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9921 0 Td
(10)Tj
1.1735 0 Td
(and)Tj
1.7292 0 Td
(20)Tj
/F15 1 Tf
0 Tc
1.1735 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.7484 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9864 0 Td
(200,)Tj
1.8765 0 Td
(in)Tj
-35.5008 -1.3039 Td
(increments)Tj
4.6941 0 Td
(of)Tj
1.0035 0 Td
(10.)Tj
1.3889 0 Td
(The)Tj
1.7745 0 Td
(values)Tj
2.6532 0 Td
(of)Tj
/F10 1 Tf
1.0091 0 Td
[()]TJ
/F9 1 Tf
0.6747 0 Td
(are)Tj
1.44 0 Td
(typical)Tj
2.8516 0 Td
(lengths)Tj
3.0784 0 Td
(for)Tj
1.3776 0 Td
(minimizers,)Tj
4.9947 0 Td
(and)Tj
1.7177 0 Td
(the)Tj
/F10 1 Tf
1.4627 0 Td
[()]TJ
/F9 1 Tf
0.737 0 Td
(values)Tj
2.6589 0 Td
(are)Tj
1.4343 0 Td
(typical)Tj
-34.9509 -1.2982 Td
(lengths)Tj
3.0897 0 Td
(of)Tj
1.0148 0 Td
(short)Tj
2.2847 0 Td
(reads.)Tj
2.5625 0 Td
(Note)Tj
2.1883 0 Td
(that)Tj
1.7745 0 Td
(in)Tj
1.0375 0 Td
(some)Tj
2.3301 0 Td
(applications,)Tj
5.2667 0 Td
(like)Tj
1.6554 0 Td
(KMC)Tj
2.4491 0 Td
(2)Tj
0.6917 0 Td
([)Tj
0.83 0.64 0.02 0 k
(8)Tj
0 g
(])Tj
1.3776 0 Td
(and)Tj
1.7291 0 Td
(Kraken)Tj
3.1691 0 Td
([)Tj
0.83 0.64 0.02 0 k
(12)Tj
0 g
(],)Tj
2.075 0 Td
(the)Tj
-34.6958 -1.2983 Td
(length)Tj
2.7269 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(window)Tj
3.4412 0 Td
(used)Tj
2.058 0 Td
(\(denoted)Tj
3.8211 0 Td
(by)Tj
/F10 1 Tf
1.1792 0 Td
[()]TJ
/F9 1 Tf
0.6859 0 Td
(there\))Tj
2.6022 0 Td
(corresponds)Tj
5.142 0 Td
(to)Tj
1.0262 0 Td
(our)Tj
/F10 1 Tf
1.6214 0 Td
[()]TJ
/F9 1 Tf
0.7483 0 Td
(parameter,)Tj
4.5411 0 Td
(and)Tj
1.7291 0 Td
(the)Tj
-33.8057 -1.3039 Td
(length)Tj
2.7269 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(minimizers)Tj
4.7792 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
1.3379 0 Td
(in)Tj
1.0375 0 Td
(KMC)Tj
2.4491 0 Td
(2\))Tj
1.0375 0 Td
(corresponds)Tj
5.1363 0 Td
(to)Tj
1.0262 0 Td
(our)Tj
/F10 1 Tf
1.627 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(parameter.)Tj
-23.1305 -1.2983 Td
(The)Tj
1.7858 0 Td
(results)Tj
2.8063 0 Td
(are)Tj
1.4513 0 Td
(summarized)Tj
5.1817 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0375 0 Td
(Fig)Tj
1.4796 0 Td
(1)Tj
0 g
(.)Tj
0.9241 0 Td
(As)Tj
1.2643 0 Td
(expected,)Tj
3.9458 0 Td
(the)Tj
1.4683 0 Td
(fraction)Tj
3.3619 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(included)Tj
3.7133 0 Td
(in)Tj
1.0318 0 Td
(the)Tj
-34.6731 -1.2982 Td
(solution)Tj
3.4809 0 Td
(set)Tj
1.3039 0 Td
(decreases)Tj
3.9685 0 Td
(with)Tj
/F10 1 Tf
1.9956 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.9751 0 Td
(It)Tj
0.856 0 Td
(is)Tj
0.8504 0 Td
(easier)Tj
2.5002 0 Td
(to)Tj
1.0261 0 Td
(hit)Tj
1.3096 0 Td
(longer)Tj
2.7836 0 Td
(sequences)Tj
4.2179 0 Td
(as)Tj
1.0148 0 Td
(they)Tj
1.9276 0 Td
(contain)Tj
3.2484 0 Td
(more)Tj
/F10 1 Tf
2.3415 0 Td
[()]TJ
/F9 1 Tf
(-mers.)Tj
-33.8001 -1.304 Td
(In)Tj
1.1055 0 Td
(addition,)Tj
3.8267 0 Td
(running)Tj
3.4979 0 Td
(times)Tj
2.3868 0 Td
(and)Tj
1.7291 0 Td
(memory)Tj
3.617 0 Td
(usage)Tj
2.4321 0 Td
(increase)Tj
3.4696 0 Td
(exponentially)Tj
5.6012 0 Td
(with)Tj
/F10 1 Tf
2.0013 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.907 0 Td
(For)Tj
/F10 1 Tf
1.6271 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(=)Tj
0.7994 0 Td
(10,)Tj
-33.6867 -1.2982 Td
(DOCKS)Tj
3.5149 0 Td
(terminated)Tj
4.6318 0 Td
(after)Tj
2.0352 0 Td
(more)Tj
2.3414 0 Td
(than)Tj
2.0296 0 Td
(2.5)Tj
1.3947 0 Td
(hours)Tj
2.5171 0 Td
(and)Tj
1.7291 0 Td
(used)Tj
2.058 0 Td
(more)Tj
2.3414 0 Td
(than)Tj
2.0296 0 Td
(1)Tj
0.6973 0 Td
(GB)Tj
1.5137 0 Td
(of)Tj
1.0148 0 Td
(memory.)Tj
3.8437 0 Td
(For)Tj
/F10 1 Tf
-33.6923 -1.2983 Td
[()]TJ
/F9 1 Tf
0.6746 0 Td
(=)Tj
0.7937 0 Td
(11)Tj
1.1679 0 Td
(and)Tj
/F10 1 Tf
1.7234 0 Td
[()]TJ
/F9 1 Tf
0.737 0 Td
(=)Tj
0.7937 0 Td
(20)Tj
1.1679 0 Td
(running)Tj
3.4866 0 Td
(time)Tj
2.0239 0 Td
(was)Tj
1.6894 0 Td
(128)Tj
1.6441 0 Td
(hours.)Tj
2.7326 0 Td
(Hence,)Tj
3.0217 0 Td
(DOCKS)Tj
3.5093 0 Td
(runtime)Tj
3.4696 0 Td
(would)Tj
2.7042 0 Td
(be)Tj
1.1452 0 Td
(prohibitively)Tj
-32.4848 -1.3039 Td
(long)Tj
1.9842 0 Td
(for)Tj
1.389 0 Td
(larger)Tj
2.5284 0 Td
(values)Tj
2.6703 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.907 0 Td
(Running)Tj
3.7474 0 Td
(times)Tj
2.3924 0 Td
(were)Tj
2.1203 0 Td
(benchmarked)Tj
5.726 0 Td
(on)Tj
1.2756 0 Td
(a)Tj
0.6519 0 Td
(single)Tj
2.5342 0 Td
(CPU)Tj
2.177 0 Td
(of)Tj
1.0148 0 Td
(a)Tj
0.652 0 Td
(20-CPU)Tj
-32.7853 -1.2983 Td
(Intel)Tj
2.0749 0 Td
(Xeon)Tj
2.3527 0 Td
(E5-2650)Tj
3.515 0 Td
(\(2.3GHz\))Tj
3.9741 0 Td
(machine)Tj
3.668 0 Td
(with)Tj
1.9956 0 Td
(384GB)Tj
2.9424 0 Td
(2133MHz)Tj
4.1952 0 Td
(RAM.)Tj
0.83 0.64 0.02 0 k
-23.5217 -1.2982 Td
(Fig)Tj
1.4853 0 Td
(1A)Tj
0 g
1.3776 0 Td
(also)Tj
1.7688 0 Td
(shows)Tj
2.6589 0 Td
(the)Tj
1.4684 0 Td
(size)Tj
1.6837 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.474 0 Td
(decycling)Tj
3.9969 0 Td
(set)Tj
1.3039 0 Td
(for)Tj
1.389 0 Td
(each)Tj
/F10 1 Tf
2.0239 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.9127 0 Td
(For)Tj
/F10 1 Tf
1.6271 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(=)Tj
0.7994 0 Td
(10)Tj
1.1678 0 Td
(and)Tj
/F10 1 Tf
1.7348 0 Td
[()]TJ
/F9 1 Tf
0.7427 0 Td
(=)Tj
0.805 0 Td
(20)Tj
1.1679 0 Td
(the)Tj
1.4683 0 Td
(number)Tj
-33.9531 -1.2983 Td
(of)Tj
1.0147 0 Td
(added)Tj
/F10 1 Tf
2.6589 0 Td
[()]TJ
/F9 1 Tf
(-mers)Tj
3.0104 0 Td
(roughly)Tj
3.3222 0 Td
(equals)Tj
2.7156 0 Td
(the)Tj
1.474 0 Td
(size)Tj
1.6837 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4684 0 Td
(decycling)Tj
4.0025 0 Td
(set,)Tj
1.525 0 Td
(while)Tj
2.3697 0 Td
(for)Tj
/F10 1 Tf
1.389 0 Td
[()]TJ
/F9 1 Tf
0.6803 0 Td
(=)Tj
0.7994 0 Td
(5)Tj
0.6973 0 Td
(and)Tj
/F10 1 Tf
1.7291 0 Td
[()]TJ
/F9 1 Tf
0.7484 0 Td
(=)Tj
0.7993 0 Td
(20)Tj
1.1736 0 Td
(it)Tj
0.788 0 Td
(is)Tj
-35.0643 -1.3039 Td
(only)Tj
1.9729 0 Td
(20%)Tj
1.9332 0 Td
(larger.)Tj
2.7552 0 Td
(For)Tj
1.6271 0 Td
(all)Tj
1.1452 0 Td
(values)Tj
2.6645 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
0.9128 0 Td
(the)Tj
1.4683 0 Td
(ratio)Tj
2.0977 0 Td
(improves)Tj
3.9401 0 Td
(as)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
0.7483 0 Td
(grows.)Tj
2.8346 0 Td
(We)Tj
1.6101 0 Td
(also)Tj
1.7688 0 Td
(compared)Tj
4.2406 0 Td
(DOCKS)Tj
-33.749 -1.2983 Td
(to)Tj
1.0261 0 Td
(a)Tj
0.6519 0 Td
(pure)Tj
2.058 0 Td
(greedy)Tj
2.8856 0 Td
(algorithm)Tj
4.1613 0 Td
(that)Tj
1.7745 0 Td
(repeatedly)Tj
4.3426 0 Td
(removes)Tj
3.5773 0 Td
(a)Tj
0.6576 0 Td
(vertex)Tj
2.6532 0 Td
(with)Tj
2.0013 0 Td
(a)Tj
0.652 0 Td
(maximum)Tj
4.371 0 Td
(hitting)Tj
2.8969 0 Td
(number,)Tj
-33.7093 -1.2982 Td
(without)Tj
3.3278 0 Td
(removing)Tj
4.0762 0 Td
(a)Tj
0.6576 0 Td
(decycling)Tj
3.9969 0 Td
(set)Tj
1.3039 0 Td
(first.)Tj
2.0296 0 Td
(For)Tj
1.6271 0 Td
(almost)Tj
2.8856 0 Td
(all)Tj
1.1452 0 Td
(combinations)Tj
5.7089 0 Td
(of)Tj
1.0148 0 Td
(\()Tj
/F10 1 Tf
[()]TJ
/F9 1 Tf
(,)Tj
/F10 1 Tf
1.2529 0 Td
[()]TJ
/F9 1 Tf
(\))Tj
1.0885 0 Td
(the)Tj
1.4684 0 Td
(size)Tj
1.6837 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4684 0 Td
(pro-)Tj
-35.7503 -1.304 Td
(duced)Tj
2.6475 0 Td
(set,)Tj
1.5307 0 Td
(runtime)Tj
3.4752 0 Td
(and)Tj
1.7292 0 Td
(memory)Tj
3.617 0 Td
(of)Tj
1.0147 0 Td
(the)Tj
1.4684 0 Td
(greedy)Tj
2.8856 0 Td
(algorithm)Tj
4.1556 0 Td
(were)Tj
2.126 0 Td
(far)Tj
1.3152 0 Td
(greater)Tj
3.0047 0 Td
(than)Tj
2.0296 0 Td
(those)Tj
2.3358 0 Td
(of)Tj
-33.3352 -1.2982 Td
(DOCKS)Tj
3.5149 0 Td
(\(see)Tj
1.7688 0 Td
(Fig)Tj
1.4797 0 Td
(A)Tj
0.9014 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0375 0 Td
(S1)Tj
1.1735 0 Td
(Text)Tj
0 g
(\).)Tj
2.5795 0 Td
(In)Tj
1.1112 0 Td
(particular,)Tj
4.337 0 Td
(the)Tj
1.4683 0 Td
(greedy)Tj
2.8856 0 Td
(algorithm's)Tj
4.7339 0 Td
(runtime)Tj
3.4752 0 Td
(was)Tj
1.7008 0 Td
(greater)Tj
3.0047 0 Td
(by)Tj
1.1849 0 Td
(a)Tj
-36.3569 -1.2983 Td
(factor)Tj
2.5398 0 Td
(of)Tj
1.0148 0 Td
(more)Tj
2.3414 0 Td
(than)Tj
2.0296 0 Td
(1000)Tj
2.1203 0 Td
(for)Tj
/F10 1 Tf
1.3889 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(=)Tj
0.7994 0 Td
(8)Tj
0.6973 0 Td
(\(taking)Tj
3.0671 0 Td
(days)Tj
1.9955 0 Td
(compared)Tj
4.2463 0 Td
(to)Tj
1.0262 0 Td
(minutes\),)Tj
4.0308 0 Td
(and)Tj
1.7291 0 Td
(it)Tj
0.788 0 Td
(increased)Tj
3.9969 0 Td
(with)Tj
/F10 1 Tf
2.0012 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
-36.4986 -1.3039 Td
(as)Tj
1.0147 0 Td
(opposed)Tj
3.5773 0 Td
(to)Tj
1.0262 0 Td
(DOCKS's)Tj
4.0932 0 Td
(runtime,)Tj
3.702 0 Td
(which)Tj
2.6476 0 Td
(decreased)Tj
4.1385 0 Td
(with)Tj
/F10 1 Tf
1.9956 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 312.4913 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(DOCKSany)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 295.4834 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(We)Tj
1.61 0 Td
(ran)Tj
1.5704 0 Td
(DOCKSany)Tj
4.9549 0 Td
(for)Tj
1.3833 0 Td
(5)Tj
/F15 1 Tf
0 Tc
0.6973 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9922 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.6859 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9922 0 Td
(11)Tj
1.1678 0 Td
(and)Tj
1.7348 0 Td
(20)Tj
/F15 1 Tf
0 Tc
1.1679 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.7484 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9921 0 Td
(200.)Tj
1.8708 0 Td
(The)Tj
1.7802 0 Td
(results)Tj
2.8119 0 Td
(for)Tj
/F10 1 Tf
1.3833 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(=)Tj
0.7994 0 Td
(10)Tj
1.1735 0 Td
(are)Tj
1.4513 0 Td
(shown)Tj
2.846 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0375 0 Td
(Fig)Tj
1.4797 0 Td
(2)Tj
0 g
-37.0089 -1.3039 Td
(and)Tj
1.7291 0 Td
(the)Tj
1.4683 0 Td
(full)Tj
1.5307 0 Td
(results)Tj
2.8063 0 Td
(are)Tj
1.4513 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0318 0 Td
(S1)Tj
1.1736 0 Td
(Table)Tj
0 g
2.4434 0 Td
(and)Tj
1.7291 0 Td
(visualized)Tj
4.1443 0 Td
(in)Tj
1.0318 0 Td
(Fig)Tj
1.4796 0 Td
(B)Tj
0.7994 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0375 0 Td
(S1)Tj
1.1735 0 Td
(Text)Tj
0 g
(.)Tj
2.2394 0 Td
(In)Tj
1.1111 0 Td
(comparison)Tj
4.9777 0 Td
(to)Tj
-33.3579 -1.2982 Td
(DOCKS)Tj
3.5149 0 Td
(\(see)Tj
1.7688 0 Td
(Fig)Tj
1.4797 0 Td
(C)Tj
0.8844 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0318 0 Td
(S1)Tj
1.1735 0 Td
(Text)Tj
0 g
(\),)Tj
2.5852 0 Td
(the)Tj
1.4683 0 Td
(produced)Tj
4.0422 0 Td
(sets)Tj
1.6668 0 Td
(are)Tj
1.4513 0 Td
(larger,)Tj
2.7553 0 Td
(especially)Tj
4.0138 0 Td
(for)Tj
1.389 0 Td
(smaller)Tj
3.1237 0 Td
(values)Tj
2.6646 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(,)Tj
-36.0281 -1.2983 Td
(and)Tj
1.7291 0 Td
(that)Tj
1.7801 0 Td
(gap)Tj
1.6328 0 Td
(grows)Tj
2.6078 0 Td
(with)Tj
/F10 1 Tf
2.0013 0 Td
[()]TJ
/F9 1 Tf
(:)Tj
0.9071 0 Td
(from)Tj
2.2053 0 Td
(10%)Tj
1.9332 0 Td
(for)Tj
/F10 1 Tf
1.3833 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(=)Tj
0.7994 0 Td
(5)Tj
0.6973 0 Td
(to)Tj
1.0261 0 Td
(60%)Tj
1.9276 0 Td
(larger)Tj
2.5284 0 Td
(for)Tj
/F10 1 Tf
1.389 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(=)Tj
0.7994 0 Td
(10.)Tj
1.3946 0 Td
(Set)Tj
1.4173 0 Td
(sizes)Tj
2.0466 0 Td
(of)Tj
1.0148 0 Td
(DOCKS)Tj
-32.5925 -1.3039 Td
(and)Tj
1.7291 0 Td
(DOCKSany)Tj
4.9549 0 Td
(are)Tj
1.4457 0 Td
(closer)Tj
2.5511 0 Td
(as)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
0.7484 0 Td
(increases)Tj
3.8324 0 Td
(and)Tj
1.7348 0 Td
(both)Tj
2.0579 0 Td
(approach)Tj
3.9515 0 Td
(the)Tj
1.4683 0 Td
(size)Tj
1.6838 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.474 0 Td
(decycling)Tj
3.9968 0 Td
(set.)Tj
1.5307 0 Td
(In)Tj
-35.189 -1.2983 Td
(terms)Tj
2.4944 0 Td
(of)Tj
1.0148 0 Td
(running)Tj
3.4979 0 Td
(time,)Tj
2.2507 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4684 0 Td
(other)Tj
2.347 0 Td
(hand,)Tj
2.4888 0 Td
(we)Tj
1.3266 0 Td
(see)Tj
1.4287 0 Td
(a)Tj
0.652 0 Td
(great)Tj
2.211 0 Td
(benefit)Tj
2.9763 0 Td
(in)Tj
1.0375 0 Td
(using)Tj
2.3868 0 Td
(DOCKSany)Tj
4.9549 0 Td
(as)Tj
1.0148 0 Td
(run-)Tj
-34.8262 -1.2982 Td
(times)Tj
2.3867 0 Td
(decrease)Tj
3.6113 0 Td
(to)Tj
1.0262 0 Td
(a)Tj
0.6519 0 Td
(small)Tj
2.3244 0 Td
(fraction)Tj
3.3619 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4683 0 Td
(DOCKS)Tj
3.515 0 Td
(running)Tj
3.4979 0 Td
(times)Tj
2.3867 0 Td
(for)Tj
1.389 0 Td
(the)Tj
1.4684 0 Td
(larger)Tj
2.5341 0 Td
(values)Tj
2.6646 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
(.)Tj
0.9127 0 Td
(We)Tj
-35.2287 -1.2983 Td
(also)Tj
1.7688 0 Td
(see)Tj
1.4286 0 Td
(reduced)Tj
3.4412 0 Td
(memory)Tj
3.617 0 Td
(usage)Tj
2.4321 0 Td
(for)Tj
1.3833 0 Td
(larger)Tj
2.5342 0 Td
(values)Tj
2.6645 0 Td
(of)Tj
/F10 1 Tf
1.0148 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(and)Tj
/F10 1 Tf
1.7291 0 Td
[()]TJ
/F9 1 Tf
0.7484 0 Td
(\(see)Tj
1.7688 0 Td
(the)Tj
1.4683 0 Td
(table)Tj
2.1317 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0375 0 Td
(S1)Tj
1.1678 0 Td
(Table)Tj
0 g
(\).)Tj
3.0104 0 Td
(Still,)Tj
-34.0325 -1.3039 Td
(DOCKSany)Tj
4.9492 0 Td
(becomes)Tj
3.685 0 Td
(impractical)Tj
4.7225 0 Td
(for)Tj
/F10 1 Tf
1.389 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.686 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9921 0 Td
(13)Tj
1.1679 0 Td
(\(runtime)Tj
3.8154 0 Td
(for)Tj
/F10 1 Tf
1.3889 0 Td
[()]TJ
/F9 1 Tf
0.686 0 Td
(=)Tj
0.7994 0 Td
(12,)Tj
/F10 1 Tf
1.3946 0 Td
[()]TJ
/F9 1 Tf
0.7484 0 Td
(=)Tj
0.7993 0 Td
(20)Tj
1.1736 0 Td
(was)Tj
1.6951 0 Td
(45)Tj
1.1735 0 Td
(days\),)Tj
2.5625 0 Td
(so)Tj
1.0885 0 Td
(we)Tj
-34.9169 -1.2983 Td
(turn)Tj
1.9672 0 Td
(to)Tj
1.0204 0 Td
(another)Tj
3.3336 0 Td
(heuristic)Tj
3.685 0 Td
(to)Tj
1.0261 0 Td
(increase)Tj
3.4753 0 Td
(runtime)Tj
3.4752 0 Td
(on)Tj
1.2756 0 Td
(the)Tj
1.4683 0 Td
(expense)Tj
3.3846 0 Td
(of)Tj
1.0148 0 Td
(larger)Tj
2.5285 0 Td
(set)Tj
1.3039 0 Td
(sizes.)Tj
ET
Q
q
1 j
1 J
0 w
11.9999 0 0 11.9999 200.0125 151.9937 cm
BT
/F0 1 Tf
1 TL
-0.0033 Tc
0 0 Td
(DOCKSanyX)Tj
ET
Q
q
1 j
1 J
0 w
10 0 0 10 200.0125 134.9858 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(We)Tj
1.61 0 Td
(tested)Tj
2.5512 0 Td
(the)Tj
1.4683 0 Td
(performance)Tj
5.3461 0 Td
(of)Tj
1.0148 0 Td
(DOCKSanyX)Tj
5.6069 0 Td
(for)Tj
/F10 1 Tf
1.389 0 Td
[()]TJ
/F9 1 Tf
0.6803 0 Td
(=)Tj
0.805 0 Td
(10,)Tj
1.3947 0 Td
(20)Tj
/F15 1 Tf
0 Tc
1.1735 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9865 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.7483 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9921 0 Td
(200)Tj
1.6498 0 Td
(and)Tj
/F10 1 Tf
1.7291 0 Td
[(")]TJ
/F9 1 Tf
0.8504 0 Td
(=)Tj
0.7993 0 Td
(5)Tj
ET
Q
q
1 j
1 J
0 w
7.4999 0 0 6.6659 512.7307 139.4645 cm
BT
/F10 1 Tf
1 TL
-0.0053 Tc
0 0 Td
[()]TJ
ET
Q
q
1 j
1 J
0 w
10 0 0 10 516.9259 134.9858 cm
BT
/F9 1 Tf
1 TL
-0.004 Tc
0 0 Td
(for)Tj
1.3889 0 Td
(0)Tj
/F15 1 Tf
0 Tc
0.6917 0 Td
()Tj
/F10 1 Tf
-0.004 Tc
0.9921 0 Td
[()]TJ
/F15 1 Tf
0 Tc
0.4875 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9922 0 Td
(5)Tj
-36.2435 -1.2982 Td
(\(Fig)Tj
1.8198 0 Td
(D)Tj
0.9525 0 Td
(in)Tj
0.83 0.64 0.02 0 k
1.0375 0 Td
(S1)Tj
1.1735 0 Td
(Text)Tj
0 g
(\).)Tj
2.5852 0 Td
(As)Tj
1.2642 0 Td
(expected,)Tj
3.9458 0 Td
(the)Tj
1.4684 0 Td
(generated)Tj
4.1385 0 Td
(set)Tj
1.3039 0 Td
(sizes)Tj
2.041 0 Td
(increase)Tj
3.4752 0 Td
(with)Tj
/F10 1 Tf
1.9956 0 Td
[(")]TJ
/F9 1 Tf
(,)Tj
1.0772 0 Td
(but)Tj
1.5533 0 Td
(the)Tj
1.4684 0 Td
(differences)Tj
4.5693 0 Td
(are)Tj
-35.8693 -1.2983 Td
(very)Tj
1.9219 0 Td
(small)Tj
2.3301 0 Td
(for)Tj
/F10 1 Tf
1.3833 0 Td
[(")]TJ
/F15 1 Tf
0 Tc
0.8503 0 Td
()Tj
/F9 1 Tf
-0.004 Tc
0.9922 0 Td
(125.)Tj
1.8765 0 Td
(On)Tj
1.5137 0 Td
(the)Tj
1.4683 0 Td
(other)Tj
2.3471 0 Td
(hand,)Tj
2.4831 0 Td
(the)Tj
1.474 0 Td
(running)Tj
3.4923 0 Td
(time)Tj
2.0296 0 Td
(improves)Tj
3.9401 0 Td
(dramatically)Tj
5.1816 0 Td
(as)Tj
/F10 1 Tf
1.0148 0 Td
[(")]TJ
/F9 1 Tf
-34.2989 -1.3039 Td
(increases)Tj
3.8324 0 Td
(and)Tj
1.7292 0 Td
(the)Tj
1.4683 0 Td
(memory)Tj
3.617 0 Td
(usage)Tj
2.4321 0 Td
(also)Tj
1.7688 0 Td
(improves)Tj
3.9401 0 Td
(with)Tj
/F10 1 Tf
1.9956 0 Td
[(")]TJ
/F9 1 Tf
(,)Tj
1.0772 0 Td
(albeit)Tj
2.3981 0 Td
(not)Tj
1.576 0 Td
(as)Tj
1.0148 0 Td
(dramatically)Tj
5.1759 0 Td
(\(see)Tj
0.83 0.64 0.02 0 k
1.7688 0 Td
(S1)Tj
-33.7943 -1.2983 Td
(Table)Tj
0 g
(\).)Tj
0.83 0.64 0.02 0 k
3.0047 0 Td
(Fig)Tj
1.4797 0 Td
(2)Tj
0 g
0.6973 0 Td
(compares)Tj
4.0762 0 Td
(the)Tj
1.4683 0 Td
(sizes)Tj
2.0466 0 Td
(of)Tj
1.0148 0 Td
(the)Tj
1.4684 0 Td
(sets)Tj
1.6667 0 Td
(generated)Tj
4.1329 0 Td
(by)Tj
1.1849 0 Td
(DOCKS,)Tj
3.7417 0 Td
(DOCKSany,)Tj
5.176 0 Td
(and)Tj
ET
Q
q
1 j
1 J
0 w
576 737.1 m
36 737.1 l
36 737.6 l
576 737.6 l
f*
36 741.2598 169.285 23.6976 re
W* n
q
169.2283 0 0 23.6409 36 741.3165 cm
q
/I0 Do
Q
Q
Q
q
0 0 612 792 re
W* n
1 j
1 J
0 w
7.9999 0 0 7.9999 450.4818 745.7952 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(Compact)Tj
4.1669 0 Td
(universal)Tj
/F7 1 Tf
4.1386 0 Td
(k)Tj
/F0 1 Tf
(-mer)Tj
2.7355 0 Td
(hitting)Tj
2.8346 0 Td
(sets)Tj
ET
Q
q
1 j
1 J
0 w
36 48.0002 m
576 48.0002 l
576 47.5002 l
36 47.5002 l
f*
0.83 0.64 0.02 0 k
142.5827 34.9228 m
295.8236 34.9228 l
h
f*
0 g
7.9999 0 0 7.9999 36 36 cm
BT
/F0 1 Tf
1 TL
-0.005 Tc
0 0 Td
(PLOS)Tj
2.8559 0 Td
(Computationa)Tj
6.1229 0 Td
(l)Tj
0.4322 0 Td
(Biology)Tj
3.4371 0 Td
(|)Tj
0.83 0.64 0.02 0 k
0.4748 0 Td
(https:/)Tj
2.6788 0 Td
(/doi.org/10.13)Tj
6.0094 0 Td
(71/journal.p)Tj
5.1166 0 Td
(cbi.1005777)Tj
0 g
6.3497 0 Td
(October)Tj
3.7276 0 Td
(2,)Tj
1.0346 0 Td
(2017)Tj
26.901 0 Td
(9)Tj
0.7654 0 Td
(/)Tj
ET
endstream
endobj
185 0 obj
<>stream
endstream
endobj
186 0 obj
<>stream
endstream
endobj
187 0 obj
<>stream
endstream
endobj
188 0 obj
<>stream
endstream
endobj
189 0 obj
<>stream
endstream
endobj
190 0 obj
<>stream
endstream
endobj
191 0 obj
<>stream
endstream
endobj
192 0 obj
<>stream
endstream
endobj
193 0 obj
<>stream
endstream
endobj
194 0 obj
<>stream
endstream
endobj
195 0 obj
<>stream
BT
66.402 0 Td
(15)Tj
ET
Q
endstream
endobj
196 0 obj
<>/XObject<>>>/CropBox[0 0 612 792]/MediaBox[0 0 612 792]/Parent 17 0 R/Annots 199 0 R/Contents 200 0 R/TrimBox[0 0 612 792]>>
endobj
198 0 obj
<>stream
xeX]%D[1EPIFEEN0Do6fD|b'9sgxA @ @ @ @ @ @ @ @ @ @ @ @ $''GFF|Ǐ|>?EC @ @ $v:uԨQgϞd6@ @ @ rLLJ!~+WǏ9. @ @ &+WJ6mڤ榡a, @ @ -[LIIɱv @ @ @ 7 Mwc @ @ %