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.

中文翻译：

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2-Max-Duo问题的$$（1.4 + \ epsilon）$$（1.4 + ϵ）-近似算法

的最大哆保鲜串映射（最大铎）的问题是充分研究的互补最低共同串分区问题，两者都具有在许多领域的应用，包括文本压缩和生物信息学。ķ -最大铎是受限制的版本最大铎，其中字母的每一个字母出现在最ķ在每个串，这是很容易还原成公知的次最大独立集（MIS上的曲线图）的问题最大度数\（\ Delta \ le 6（k-1）\）。特别是2- Max-Duo然后，针对有界图上的MIS问题，使用最新的近似算法，可以将其任意近似地近似为1.8 。2- Max-Duo被证明是APX-hard的，最近，对于任何\（\ epsilon> 0 \），都提出了\（（1.6 + \ epsilon）\） -近似算法。在本文中，我们提出了一种顶点度缩减技术，在此基础上，我们表明2 -Max-Duo可以任意接近1.4。