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A space efficient algorithm for the constrained heaviest common subsequence problem

Published: 28 March 2008 Publication History

Abstract

Let Σ be an alphabet. For each letter in Σ a positive weight is assigned to it. The weight of a string S over Σ is defined as the sum of the weights of the letters in S. For two strings X, Y, and a constrained string P over an alphabet Σ, the constrained heaviest common subsequence problem for two strings X and Y with respect to P is to find a sequence Z such that Z is the heaviest, i.e., having the largest weight, common subsequence for X and Y and P is a subsequence of Z. In this paper an O(|X||Y||Z|) time and O((|X|+|Y|)|P|) space algorithm for the constrained heaviest common subsequence problem of two strings is presented, where |X|, |Y|, and |P| denote the lengths of string X, Y, P, respectively.

References

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A. Apostolico, String editing and longest common subsequences, in: G. Rozenberg and A. Salomaa (Eds.), Linear Modeling: Background and Application, in: Handbook of Formal Languages, Vol. 2, Springer-Verlag, Berlin, 1997.
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A. Apostolico, Chapter 13: General pattern matching, in: M. J. Atallah (Ed.), Handbook of Algorithms and Theory of Computation, CRC, Boca Raton, FL, 1998.
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L. Bergroth, H. Hakonen, and T. Raita, A survey of longest common subsequence algorithms, in: SPIRE, A Coruña, Spain, 2000.
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F. Y. L. Chin, A. De Santis, A. L. Ferrara, N. L. Ho, and S. K. Kim, A simple algorithm for the constrained sequence problems, Information Processing Letters 90 (2004) 175--179.
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T. Cormen, C. Leiserson, R. Rivest, and C. Stein, Section 15.4: Longest common subsequence, Introduction to Algorithms (second edition), MIT Press, Cambridge, MA, 2001.
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D. Hirschberg, Serial computations of Levenshtein distances, in: A. Apostolico and Z. Galil (Eds.), Pattern Matching Algorithms, Oxford University Press, Oxford, 1997.
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R. Li, A linear space algorithm for the heaviest common subsequence problem, to appear.
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R. Li, R. Shick, and D. Smiley, An algorithm for the constrained heaviest common subsequence problem, Congressus Numerantium 174 (2005) 123--128.
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  • (2015)Examining the effectiveness of using concolic analysis to detect code clonesProceedings of the 30th Annual ACM Symposium on Applied Computing10.1145/2695664.2695929(1610-1615)Online publication date: 13-Apr-2015

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    cover image ACM Other conferences
    ACMSE '08: Proceedings of the 46th annual ACM Southeast Conference
    March 2008
    548 pages
    ISBN:9781605581057
    DOI:10.1145/1593105
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    Publication History

    Published: 28 March 2008

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    Author Tags

    1. constrained heaviest common subsequence
    2. constrained longest common subsequence
    3. heaviest common subsequence
    4. longest common subsequence

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    ACM SE08
    ACM SE08: ACM Southeast Regional Conference
    March 28 - 29, 2008
    Alabama, Auburn

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    • (2015)Examining the effectiveness of using concolic analysis to detect code clonesProceedings of the 30th Annual ACM Symposium on Applied Computing10.1145/2695664.2695929(1610-1615)Online publication date: 13-Apr-2015

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