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Minimum common string partition revisited

Author

Listed:
  • Haitao Jiang

    (Montana State University
    Shandong University)

  • Binhai Zhu

    (Montana State University)

  • Daming Zhu

    (Shandong University)

  • Hong Zhu

    (East China Normal University)

Abstract

Minimum Common String Partition (MCSP) has drawn much attention due to its application in genome rearrangement. In this paper, we investigate three variants of MCSP: MCSP c , which requires that there are at most c elements in the alphabet; d-MCSP, which requires the occurrence of each element to be bounded by d; and x-balanced MCSP, which requires the length of blocks being in range (n/k−x,n/k+x), where n is the length of the input strings, k is the number of blocks in the optimal common partition and x is a constant integer. We show that MCSP c is NP-hard when c≥2. As for d-MCSP, we present an FPT algorithm which runs in O ∗((d!)2k ) time. As it is still unknown whether an FPT algorithm only parameterized on k exists for the general case of MCSP, we also devise an FPT algorithm for the special case x-balanced MCSP parameterized on both k and x.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:23:y:2012:i:4:d:10.1007_s10878-010-9370-2
    DOI: 10.1007/s10878-010-9370-2
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    Cited by:

    1. 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.
    2. Blum, Christian & Lozano, José A. & Davidson, Pinacho, 2015. "Mathematical programming strategies for solving the minimum common string partition problem," European Journal of Operational Research, Elsevier, vol. 242(3), pages 769-777.

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