An improved algorithm for sorting by block-interchanges based on permutation groups

Given a chromosome represented by a permutation of genes, a block-interchange is proposed as a generalized transposition that affects the chromosome by swapping two non-intersecting segments of genes. The problem of sorting by block-interchanges is to find a minimum series of block-interchanges for sorting one chromosome into another. In this paper, we present an time algorithm for solving the problem of sorting by block-interchanges, which improves a previous algorithm of O(δn) time proposed by Lin et al. (2005) [14], where n is the number of genes and δ is the minimum number of block-interchanges required to sort a chromosome.