When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2017.66
URN: urn:nbn:de:0030-drops-82120
URL: http://drops.dagstuhl.de/opus/volltexte/2017/8212/
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Xu, Yao ; Chen, Yong ; Lin, Guohui ; Liu, Tian ; Luo, Taibo ; Zhang, Peng

### A (1.4 + epsilon)-Approximation Algorithm for the 2-Max-Duo Problem

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### Abstract

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 \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. 2-Max-Duo was proved APX-hard and 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 close to 1.4.

### BibTeX - Entry

@InProceedings{xu_et_al:LIPIcs:2017:8212,
author =	{Yao Xu and Yong Chen and Guohui Lin and Tian Liu and Taibo Luo and Peng Zhang},
title =	{{A (1.4 + epsilon)-Approximation Algorithm for the 2-Max-Duo Problem}},
booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages =	{66:1--66:12},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-054-5},
ISSN =	{1868-8969},
year =	{2017},
volume =	{92},
editor =	{Yoshio Okamoto and Takeshi Tokuyama},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},