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On the Exact Block Cover Problem

  • Haitao Jiang
  • Bing Su
  • Mingyu Xiao
  • Yinfeng Xu
  • Farong Zhong
  • Binhai Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8546)

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 *(2 k ) 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.

Keywords

Bipartite Graph Genome Rearrangement Dynamic Programming Algorithm Edit Distance Input String 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Haitao Jiang
    • 1
  • Bing Su
    • 2
  • Mingyu Xiao
    • 3
  • Yinfeng Xu
    • 4
  • Farong Zhong
    • 5
  • Binhai Zhu
    • 6
  1. 1.School of Computer Science and TechnologyShandong UniversityJinanChina
  2. 2.School of Economics and ManagementXi’an Technological UniversityXi’anChina
  3. 3.School of Computer Science and EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina
  4. 4.Business SchoolSichuan UniversityChengduChina
  5. 5.College of Math, Physics and Information TechnologyZhejiang Normal UniversityJinhuaChina
  6. 6.Department of Computer ScienceMontana State UniversityBozemanUSA

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