A 14/11-approximation algorithm for sorting by short block-moves

Abstract

Block-move is one of the popular operations for genome rearrangement. A short block-move is an operation on a permutation that moves an element at most two positions away from its original position. Heath and Vergara investigated the problem of finding a minimum-length sorting sequence of short block-moves for a given permutation and devised a 4/3-approximation algorithm. In this paper, we present a new 14/11- approximation algorithm for this problem. Firstly, we devise an exact polynomial time algorithm for sorting a special kind of sub-permutations called umbrella; then we split the permutation into a series of related umbrellas and sort them greedily. We obtain a new lower bound of the short block-move distance by exploiting the properties of five kinds of sub-permutations. After some complicated analysis, we prove that the approximation ratio of the new algorithm is at most 14/11. © Science China Press and Springer-Verlag Berlin Heidelberg 2010.