Sorting with Forbidden Intermediates

A wide range of applications, most notably in comparative genomics, in-volve the computation of a shortest sorting sequence of operations for a givenpermutation, where the set of allowed operations is fixed beforehand. Suchsequences are useful for instance when reconstructing potential scenarios ofevolution between species, or when trying to assess their similarity. We revisitthose problems by adding a new constraint on the sequences to be computed:they must avoid a given set of forbidden intermediates, which correspond tospecies that cannot exist because the mutations that would be involved intheir creation are lethal. We initiate this study by focusing on the case wherethe only mutations that can occur are exchanges of any two elements in thepermutations, and give a polynomial time algorithm for solving that problemwhen the permutation to sort is an involution.