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We focused our experiments on organelle genomes and generated datasets of three genomes with 100 genes for each genome (larger genome sizes were also tested). We first generated trees with three leaves and one internal node, assigned the identity permutation on the internal node and generate the three leaves by applying rearrangement events along each edge respectively. The number of events on each edge is governed by two parameters: the number of overall evolutionary events and the tree shape.

All possible inversions that appear as the first step in the sorting. Fig. 2 gives one example of sorting reversals: there are eight possible inversions that bring G2 one step closer to G1 (the identity genome). This algorithm can be easily extended to enumerate all Improving Inversion Median Computation G2 : −1 1 −2 −3 −4 −5 2 3 4 5 G1 : 1 6 2 3 4 33 5 indicates start and end points of a reversal 7 8 Fig. 2. Eight sorting reversals that bring (-1 -2 -3 -4 -5) one step closer to (1 2 3 4 5) minimum sorting sequences by identifying every sorting reversals at each step of the sorting.

Exemplar Model. For the exemplar model, we use the same strategy (iteratively match the genes of an LCS ), except that in this case we must make sure that only one gene from each family is matched on each genome. Therefore, at each iteration, and for each gene g present in the LCS (and thus kept in the matching), we remove all the other occurrences of g in both genomes. Let us call this heuristic IILCS EX. We have tested both IILCS MM and IILCS EX under, respectively, the maximum matching and exemplar models.

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