Constraint Programming Models for Transposition Distance Problem

Genome Rearrangements addresses the problem of finding the minimum number of global operations, such as transpositions, reversals, fusions and fissions that transform a given genome into another. In this paper we deal with transposition events, which are events that change the position of two contiguous block of genes in the same chromosome. The transposition event generates the transposition distance problem, that is to find the minimum number of transposition that transform one genome (or chromosome) into another. Although some tractables instances were found [20, 14], it is not known if an exact polynomial time algorithm exists. Recently, Dias and Souza [9] proposed polynomial-sized Integer Linear Programming (ILP) models for rearrangement distance problems where events are restricted to reversals, transpositions or a combination of both. In this work we devise a slight different approach. We present some Constraint Logic Programming (CLP) models for transposition distance based on known bounds to the problem.