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Figure 2 | Algorithms for Molecular Biology

Figure 2

From: Sampling solution traces for the problem of sorting permutations by signed reversals

Figure 2

Building a 8-trace with 4-traces. This schema shows a sequence of reversals that optimally sorts π0 = (−7, + 8,−3, + 2, + 6,−5,−1, + 4) into π8 = ( + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8). This sequence of reversals is represented by the 8-trace {1,−,6,8}{1,−,3,5,6}{2,5,6}{6}{8}|{1,−,7}{3,4}|{3,−,6}. This 8-trace can be obtained by the application of the reversals of the 4-trace C = {2,5,6}{3,4}{6}|{3,−,6} (it sorts π4into π8) to the sequence of reversals of the 4-trace A = {1,−,6,8}{1,−,3,5,6}{8}|{1,−,7} (it sorts π0into π4). The algorithm DFA can be used to obtain the two 4-traces which sort π0into π4and the two 4-traces which sort π4into π8. Combining these 4-traces, we obtain all 8-traces of solutions which sort π0into π8and have π4as an intermediary permutation.

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