Implementing algorithms for sorting by strip swaps

Abstract

Genome rearrangement problems in computational biology have been modeled as combinatorial optimization problems related to the familiar problem of sorting, namely transforming arbitrary permutations to the identity permutation. When a permutation is viewed as the string of integers from 1 through n, any substring in it that is also a substring in the identity permutation will be called a strip. The objective in the combinatorial optimization problems arising from the applications is to obtain the identity permutation from an arbitrary permutation in the least number of a particular chosen strip operation. Among the strip operations which have been investigated thus far in the literature are strip moves, transpositions, reversals, and block interchanges. However, it is important to note that most of the existing research on sorting by strip operations has been focused on obtaining hardness results or designing approximation algorithms, with little work carried out thus far on the implementation of the proposed approximation algorithms. In this paper, two new algorithms for sorting by strip swaps are presented. The first algorithm takes a greedy approach and selects at each step a strip swap that reduces the number of strips the most, and puts maximum strips in their correct positions. The second algorithm brings the closest consecutive pairs together at each step. Approximation ratios for these two algorithms are experimentally estimated.