A (1.4+Epsilon)-Approximation Algorithm For The 2-Max-Duo Problem

The maximum duo-preservation string mapping (MAX-DUO) problem is the complement of the well studied minimum common string partition problem, both of which have applications in many fields including text compression and bioinformatics. k-MAX-DUO is the restricted version of MAX-DUO, where every letter of the alphabet occurs at most k times in each of the strings, which is readily reduced into the well known maximum independent set (MIS) problem on a graph of maximum degree Delta <= 6(k - 1). In particular, 2-MAX-DUO can then be approximated arbitrarily close to 1.8 using the state-of-the-art approximation algorithm for the MIS problem on bounded-degree graphs. 2-MAX-DUO was proved APX-hard and very recently a (1.6 + C)-approximation algorithm was claimed, for any C > 0. In this paper, we present a vertex-degree reduction technique, based on which, we show that 2-MAX-DUO can be approximated arbitrarily close to 1.4.