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Solving Hard Computational Problems Efficiently: Asymptotic Parametric Complexity 3-Coloring Algorithm

Figure 2

Backtracking vs. proposed algorithm.

Runtime analysis of the backtracking (brute force plus heuristic) () vs. the proposed parametric algorithm () over random planar graphs between 10 and 100 vertices. Plot (a) shows the running times as a function of the number of vertices for both kinds of instance types and for both algorithms. Plot (b) shows the proportion of 3-colorable and non-3-colorable graphs over the total number of graphs per number of vertices. Plots (c) and (d) also show the running times as a function of the number of vertices discriminated by the instance types (yes-or-no) so that subtle differences can be observed. Plots (e) and (f) also show the running times but as a function of the average degree and instance type.

Figure 2

doi: https://doi.org/10.1371/journal.pone.0053437.g002