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On the generalized constrained longest common subsequence problems

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Abstract

We investigate four variants of the longest common subsequence problem. Given two sequences X, Y and a constrained pattern P of lengths m, n, and ρ, respectively, the generalized constrained longest common subsequence (GC-LCS) problems are to find a longest common subsequence of X and Y including (or excluding) P as a subsequence (or substring). We propose new dynamic programming algorithms for solving the GC-LCS problems in O(mn ρ) time. We also consider the case where the number of constrained patterns is arbitrary.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, Taipei, 106, Taiwan

    Yi-Ching Chen

  2. Department of Computer Science and Information Engineering, Graduate Institute of Biomedical Electronics and Bioinformatics, Graduate Institute of Networking and Multimedia, National Taiwan University, Taipei, 106, Taiwan

    Kun-Mao Chao

Authors
  1. Yi-Ching Chen
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  2. Kun-Mao Chao
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Corresponding author

Correspondence to Kun-Mao Chao.

Additional information

This research was supported in part by NSC grants NSC 95-2221-E-002-126-MY3 and NSC 97-2221-E-002-097-MY3 from the National Science Council, Taiwan.

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Chen, YC., Chao, KM. On the generalized constrained longest common subsequence problems. J Comb Optim 21, 383–392 (2011). https://doi.org/10.1007/s10878-009-9262-5

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  • DOI: https://doi.org/10.1007/s10878-009-9262-5

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