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Restricted LCS

  • Conference paper
String Processing and Information Retrieval (SPIRE 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6393))

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Abstract

The Longest Common Subsequence (LCS) of two or more strings is a fundamental well-studied problem which has a wide range of applications throughout computational sciences. When the common subsequence must contain one or more constraint strings as subsequences, the problem becomes the Constrained LCS (CLCS) problem. In this paper we consider the Restricted LCS (RLCS) problem, where our goal is finding a longest common subsequence between two or more strings that does not contain a given set of restriction strings as subsequences. First we show that in case of two input strings and an arbitrary number of restriction strings the RLCS problem is NP-hard. Afterwards, we present a dynamic programming solution for RLCS and we show that this algorithm implies that RLCS is in FPT when parameterized by the total length of the restriction strings. In the last part of this paper we present two approximation algorithms for the hard variants of the problem.

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Author information

Authors and Affiliations

  1. Bar-Ilan University, Israel

    Zvi Gotthilf & Moshe Lewenstein

  2. University of Haifa, Israel

    Danny Hermelin

  3. University of Haifa, Israel, and NYU-Poly, USA

    Gad M. Landau

Authors
  1. Zvi Gotthilf
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  2. Danny Hermelin
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  3. Gad M. Landau
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  4. Moshe Lewenstein
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Editor information

Editors and Affiliations

  1. School of Physics and Mathematics, Edificio "B", Universidad Michoacana, Ciudad Universitaria, 5800, Morelia, Mich., Mexico

    Edgar Chavez

  2. Dept. of Computer Science and Enginerring, University of California, 92521, Riverside, CA, USA

    Stefano Lonardi

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© 2010 Springer-Verlag Berlin Heidelberg

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Gotthilf, Z., Hermelin, D., Landau, G.M., Lewenstein, M. (2010). Restricted LCS. In: Chavez, E., Lonardi, S. (eds) String Processing and Information Retrieval. SPIRE 2010. Lecture Notes in Computer Science, vol 6393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16321-0_26

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  • DOI: https://doi.org/10.1007/978-3-642-16321-0_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16320-3

  • Online ISBN: 978-3-642-16321-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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