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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 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.

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Acknowledgements

This research is supported by the NSERC Canada. Additionally, Chen is supported by the National Natural Science Foundation of China Grant No.’s 11971139, 11771114 and 11571252, and the China Scholarship Council Grant No. 201508330054; Liu is supported by the National Natural Science Foundation of China Grant No. 61370052; Luo is supported by the National Natural Science Foundation of China Grant No. 71701162, the Humanities and Social Science Foundation of Ministry of Education of China Grant No. 18YJC630114, and the Youth Innovation Team of Shaanxi Universities; Su is supported partially by the Humanities and Social Science Foundation of Ministry of Education of China Grant No. 18YJAZH080 and Science and Technology Department of Shaanxi Province Grant No. 2020JQ-654; Zhang is supported by the National Natural Science Foundation of China Grant No.’s 61972228 and 61672323.

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou, Zhejiang, China

    Yong Chen

  2. Department of Computing Science, University of Alberta, Edmonton, AB T6G 2E8, Canada

    Guohui Lin

  3. Key Laboratory of High Confidence Software Technologies (MOE), Department of Computer Science and Technology, Peking University, Beijing, China

    Tian Liu

  4. School of Economics and Management, Xidian University, Xi’an, Shaanxi, China

    Taibo Luo

  5. School of Economics and Management, Xi’an Technological University, Xi’an, Shaanxi, China

    Bing Su

  6. Department of Computer Science, Kettering University, Flint, MI, USA

    Yao Xu

  7. School of Computer Science and Technology, Shandong University, Jinan, Shandong, China

    Peng Zhang

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  1. Yong Chen
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  2. Guohui Lin
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  3. Tian Liu
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Correspondence to Guohui Lin.

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An extended abstract appears in Proceedings of the 28th International Symposium on Algorithms and Computation (ISAAC 2017). LIPICS 92, Article No. 66, pp. 66:1–66:12.

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Chen, Y., Lin, G., Liu, T. et al. A \((1.4 + \epsilon )\)-approximation algorithm for the 2-Max-Duo problem. J Comb Optim 40, 806–824 (2020). https://doi.org/10.1007/s10878-020-00621-0

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  • DOI: https://doi.org/10.1007/s10878-020-00621-0

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