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

Author

Listed:
  • Yong Chen

    (Hangzhou Dianzi University)

  • Guohui Lin

    (University of Alberta)

  • Tian Liu

    (Peking University)

  • Taibo Luo

    (Xidian University)

  • Bing Su

    (Xi’an Technological University)

  • Yao Xu

    (Kettering University)

  • Peng Zhang

    (Shandong University)

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

Suggested Citation

  • Yong Chen & Guohui Lin & Tian Liu & Taibo Luo & Bing Su & Yao Xu & Peng Zhang, 2020. "A $$(1.4 + \epsilon )$$ ( 1.4 + ϵ ) -approximation algorithm for the 2-Max-Duo problem," Journal of Combinatorial Optimization, Springer, vol. 40(3), pages 806-824, October.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:3:d:10.1007_s10878-020-00621-0
    DOI: 10.1007/s10878-020-00621-0
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    References listed on IDEAS

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    1. Haitao Jiang & Binhai Zhu & Daming Zhu & Hong Zhu, 2012. "Minimum common string partition revisited," Journal of Combinatorial Optimization, Springer, vol. 23(4), pages 519-527, May.
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