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Figure 1.

An original MUL tree used to test the MTRT algorithm.

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Figure 2.

The obtained MUL tree by applying MTRT on the triplets extracted from the MUL tree shown in Figure 1.

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Figure 3.

An original MUL tree on violet species with 20 duplications.

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Figure 4.

The obtained MUL tree by applying MTRT on the triplets extracted from the MUL tree shown in Figure 3.

This MUL tree has 18 duplications.

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Figure 5.

An original MUL tree on flowering plants with 7 duplications.

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Figure 6.

The obtained MUL tree by applying MTRT on the triplets extracted from the MUL tree shown in Figure 5.

This MUL tree has 5 duplications.

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Figure 7.

Comparing MUL trees using triplet distance.

(a) The MUL tree , (b) The MUL tree is consistent with . The MUL tree has less duplication than and is consistent with the triplet which is not contained in . So, , (c) The MUL tree , (d) The MUL tree is consistent with . The MUL trees and have the same number of duplications and .

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Figure 8.

A MUL tree which has three different triplets .

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Figure 9.

Two different MUL trees with tha same multiset of triplets .

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Table 1.

The results of MTRT algorithm on simulated datasets.

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Figure 10.

Steps of MTRT.

(a) The auxiliary graph corresponding to , (b) , (c) The auxiliary graph , (d) The auxiliary graph , (e) A smallest MUL tree produced by MTRT algorithm.

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Figure 11.

Pseudocode of the MTRT algorithm.

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