Abstract

The breakpoint distance between two n-permutations is the number of pairs that appear consecutively in one but not in the other. In the median problem for breakpoints one is given a set of permutations and has to construct a permutation that minimizes the sum of breakpoint distances to all the original ones. Recently, the problem was suggested as a model for determining the evolutionary history of several species based on their gene orders. We show that the problem is already NP-hard for three permutations, and that this result holds both for signed and for unsigned permutations.

Citations