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 (MCSP) 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 ∆ ≤ 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. 2-Max-Duo was proved APX-hard and very recently a (1.6 + )-approximation was claimed, for any > 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. 1998 ACM Subject Classification F.2.2 Pattern matching; G.2.1 Combinatorial algorithms; G.4 Algorithm design and analysis