Polynomial time algorithm for constructing vertex-disjoint paths in transposition graphs

Abstract

A transposition graph is a Cayley graph in which each vertex corresponds to a permutation and an edge is placed between permutations iff they differ by exactly one transposition. In this article, we propose an efficient algorithm to find a collection of vertex-disjoint paths connecting a given source vertex s and a given set of destination vertices D. The running time of the algorithm is polynomial in the number of destination vertices, and the resultant path connecting s and each destination is longer than the distance to the destination by at most 16. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010