We prove that the problem of sorting a permutation by the minimum number of reversals is NP-hard, thus answering a major question on the complexity of a problem which has widely been studied in the last years. The proof is based on the strong relationship between this problem and the problem of finding the maximum number of edge-disjoint alternating cycles in a suitably-defined bicolored graph. For this latter problem we derive a number of structural properties, that can be used for showing its… CONTINUE READING