A $$(1.4 + \epsilon )$$(1.4+ϵ) -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 $$\Delta \le 6(k-1)$$ . 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 $$(1.6 + \epsilon )$$ -approximation algorithm was claimed, for any $$\epsilon > 0$$ . 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.