Sorting by short swaps.

A short swap is an operation on a permutation that switches two elements that have at most one element between them. This paper investigates the problem of finding a minimum-length sorting sequence of short swaps for a given permutation. A polynomial-time 2-approximation algorithm for this problem is presented, and bounds for the short-swap diameter (the length of the longest minimum sorting sequence among all permutations of a given length) are also obtained.