Exponential and polynomial time algorithms for the minimum common string partition problem

  • Authors:

  • Bin Fu;Haitao Jiang;Boting Yang;Binhai Zhu

  • Affiliations:

  • Department of Computer Science, University of Texas-Pan American, Edinburg, TX;School of Computer Science and Technology, Shandong University, Jinan Shandong, China;Department of Computer Science University of Regina Regina, Saskatchewan Canada, Canada;Department of Computer Science, Montana State University, Bozeman, MT

  • Venue:
  • COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
  • Year:
  • 2011

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Abstract

Given two strings S and S′ of the same length, the Minimum Common String Partition (MCSP) is to partition them into the minimum number of strings S = S1 . S2 . . . Sk and S′= S′1. S′2. . . S′k such that the substrings 〈S′1, S′2, . . . , S′k〉 is a permutation of 〈S1, S1, . . . , Sk. MCSP is an NP-complete problem originating from computational genomics. There exists constant-factor approximations for some special cases, but the factors are impractical. On exact solutions, it is open whether there exists an FPT algorithm for the general case and some inefficient FPT algorithms for very special cases. In this paper, we present an O(2nnO(1)) time algorithm for the general case. We also show an O(n(log n)2) time algorithm which solves the case for almost all strings S and S′if the length of each block in their minimum common partition is at least d0 log n/log t for some positive constant d0, where t is the size of the alphabet Σ.