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The maximum duo-preservation string mapping (Max-Duo) problem is thecomplement of the well studied minimum common string partition (MCSP) problem,both of which have applications in many fields including text compression andbioinformatics. $k$-Max-Duo is the restricted version of Max-Duo, where everyletter of the alphabet occurs at most $k$ times in each of the strings, whichis readily reduced into the well known maximum independent set (MIS) problem ona graph of maximum degree $\Delta \le 6(k-1)$. In particular, $2$-Max-Duo canthen be approximated arbitrarily close to $1.8$ using the state-of-the-artapproximation algorithm for the MIS problem. $2$-Max-Duo was proved APX-hardand very recently a $(1.6 + \epsilon)$-approximation 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 closeto $1.4$.

A $(1.4 + \epsilon)$-approximation algorithm for the $2$-Max-Duo problem