3.2-Approximation for Reversal Distance toward String Adjacency Recovery.

Abstract

Rearrangement distance problems seek to measure evolutionary distance between genomes by the minimal number of rearrangement events transforming one genome into another, offering tools for comparative genomics. To reflect the importance that gene adjacency is conservative in genome evolution, SBRR (Sorting By Reversals to Recover Adjacencies) asks to find a shortest reversal sequence transforming one string into one that shares a common set of adjacencies with the other string. SBRR is NP-hard and APX-hard, admits a 4-approximation algorithm, an approximation standing for several years. In this paper, a polynomial time 3.2-approximation algorithm for SBRR is presented. An SBRR instance is given to show that 3.2 is a tight approximation ratio our algorithm can achieve. The technique in this paper applies to designing algorithms for other string rearrangement distance problems for adjacency recovery.