On recovering syntenic blocks from comparative maps

Abstract

A genomic map is represented by a sequence of gene markers, and a gene marker can appear in several different genomic maps, in either positive or negative form. A strip (syntenic block) is a sequence of distinct markers that appears as subsequences in two or more maps, either directly or in reversed and negated form. Given two genomic maps G and H, the problem Maximal Strip Recovery (MSR) is to find two subsequences G′ and H′ of G and H, respectively, such that the total length of disjoint strips in G′ and H′ is maximized. Previously only a heuristic was provided for this problem, which does not guarantee finding the optimal solution, and it was unknown whether the problem is NP-hard or polynomially solvable. In this paper, we develop a factor-4 polynomial-time approximation algorithm for the problem, and show that several close variants of the problem are intractable.