A (1.4+ϵ)-approximation algorithm for the 2-Max-Duo problem - Chen, Yong; Lin, Guohui; Liu, Tian; Luo, Taibo; Su, Bing; Xu, Yao; Zhang, Peng (Journal of combinatorial optimization, 2020)
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 Δ ≤ 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 + ϵ ) -approximation algorithm was claimed, for any ϵ > 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.