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Efficient polynomial-time algorithms for the constrained LCS problem with strings exclusion

Author

Listed:
  • Hsing-Yen Ann

    (National Center for High-Performance Computing)

  • Chang-Biau Yang

    (National Sun Yat-sen University)

  • Chiou-Ting Tseng

    (National Sun Yat-sen University)

Abstract

In this paper, we revisit a recent variant of the longest common subsequence (LCS) problem, the string-excluding constrained LCS (STR-EC-LCS) problem, which was first addressed by Chen and Chao (J Comb Optim 21(3):383–392, 2011). Given two sequences $$X$$ and $$Y$$ of lengths $$m$$ and $$n,$$ respectively, and a constraint string $$P$$ of length $$r,$$ we are to find a common subsequence $$Z$$ of $$X$$ and $$Y$$ which excludes $$P$$ as a substring and the length of $$Z$$ is maximized. In fact, this problem cannot be correctly solved by the previously proposed algorithm. Thus, we give a correct algorithm with $$O(mnr)$$ time to solve it. Then, we revisit the STR-EC-LCS problem with multiple constraints $$\{ P_1, P_2, \ldots , P_k \}.$$ We propose a polynomial-time algorithm which runs in $$O(mnR)$$ time, where $$R = \sum _{i=1}^{k} |P_i|,$$ and thus it overthrows the previous claim of NP-hardness.

Suggested Citation

  • Hsing-Yen Ann & Chang-Biau Yang & Chiou-Ting Tseng, 2014. "Efficient polynomial-time algorithms for the constrained LCS problem with strings exclusion," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 800-813, November.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:4:d:10.1007_s10878-012-9588-2
    DOI: 10.1007/s10878-012-9588-2
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    1. Yi-Ching Chen & Kun-Mao Chao, 2011. "On the generalized constrained longest common subsequence problems," Journal of Combinatorial Optimization, Springer, vol. 21(3), pages 383-392, April.
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