A column-generation based branch-and-bound algorithm for sorting by reversals

We consider the problem of sorting a permutation by reversals (SBR), calling for the minimum number of reversals transforming a given permutation of f1; : : : ; ng into the identity permutation. SBR was inspired by computational biology applications , in particular genome rearrangement. We propose an exact branch-and-bound algorithm for SBR. A lower bound is computed by solving a linear program with a possibly exponential (in n) number of variables, by using column generation techniques. An eeective branching scheme is described, which is combined with a greedy algorithm capable of producing near{optimal solutions. The algorithm presented can solve to optimality SBR instances of considerably larger size with respect to previous existing methods.