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On the Exact Block Cover Problem

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Book cover Algorithmic Aspects in Information and Management (AAIM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8546))

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Abstract

Minimum Common String Partition (MCSP) has drawn a lot of attention due to its application in genome rearrangement. The best approximation algorithm has a factor O(lognlog* n) and it was shown most recently that it is FPT (but with a very high running time). In this paper, we consider the decision version of the one-sided MCSP problem (formally called the exact block cover problem); namely, when one sequence is already partitioned into k blocks, how to decide whether the other sequence can be partitioned accordingly. While this decision problem is obviously in FPT, we show interesting results in this paper: (1) If each letter is allowed to appear at most twice (or three times), then the problem is polynomially solvable, (2) There is an FPT algorithm which runs in O *(2k) time, improving the trivial bound of O *(k!), and (3) If |Σ| = c, c being a constant at least 2, then the problem is NP-complete.

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Author information

Authors and Affiliations

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

    Haitao Jiang

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

    Bing Su

  3. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, China

    Mingyu Xiao

  4. Business School, Sichuan University, Chengdu, Sichuan, China

    Yinfeng Xu

  5. College of Math, Physics and Information Technology, Zhejiang Normal University, Jinhua, China

    Farong Zhong

  6. Department of Computer Science, Montana State University, Bozeman, MT, 59717, USA

    Binhai Zhu

Authors
  1. Haitao Jiang
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  2. Bing Su
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  3. Mingyu Xiao
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  4. Yinfeng Xu
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  5. Farong Zhong
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  6. Binhai Zhu
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Editor information

Editors and Affiliations

  1. School of Computing Science, Simon Fraser University, V5A 1S6, Burnaby, BC, Canada

    Qianping Gu  & Pavol Hell  & 

  2. Department of Computer Science, University of Regina, S4S 0A2, Regina, SK, Canada

    Boting Yang

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Jiang, H., Su, B., Xiao, M., Xu, Y., Zhong, F., Zhu, B. (2014). On the Exact Block Cover Problem. In: Gu, Q., Hell, P., Yang, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2014. Lecture Notes in Computer Science, vol 8546. Springer, Cham. https://doi.org/10.1007/978-3-319-07956-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-07956-1_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07955-4

  • Online ISBN: 978-3-319-07956-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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