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Annual Symposium on Combinatorial Pattern Matching

CPM 2003: Combinatorial Pattern Matching pp 225–236Cite as

Sparse LCS Common Substring Alignment

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2676))

Abstract

The “Common Substring Alignment” problem is defined as follows. The input consists of a set of strings S 1, S 2 ... S c, with a common substring appearing at least once in each of them, and a target string T. The goal is to compute similarity of all strings S i with T, without computing the part of the common substring over and over again. In this paper we consider the Common Substring Alignment problem for the LCS (Longest Common Subsequence) similarity metric. Our algorithm gains its efficiency by exploiting the sparsity inherent to the LCS problem. Let Y be the common substring, n be the size of the compared sequences, L y be the length of the LCS of T and Y, denoted |LCS[T, Y]|, and L be max{|LCS[T, S i]|}. Our algorithm consists of an O(nL y) time encoding stage that is executed once per common substring, and an O(L) time alignment stage that is executed once for each appearance of the common substring in each source string. The additional running time depends only on the length of the parts of the strings that are not in any common substring.

partially supported by NSF grant CCR-0104307, by the Israel Science Foundation grant 282/01, by the FIRST Foundation of the Israel Academy of Science and Humanities, and by IBM Faculty Partnership Award.

On Education Leave from the IBM T.J. Watson Research Center; michal@cs.haifa.ac.il; partially supported by the Israel Science Foundation grant 282/01, and by the FIRST Foundation of the Israel Academy of Science and Humanities.

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Author information

Authors and Affiliations

  1. Department of Computer and Information Science, Polytechnic University, Six MetroTech Center, Brooklyn, NY, 11201-3840

    Gad M. Landau

  2. Department of Computer Science, Haifa University, Haifa, 31905, Israel

    Gad M. Landau & Michal Ziv-Ukelson

  3. IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598

    Baruch Schieber & Michal Ziv-Ukelson

Authors
  1. Gad M. Landau
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  2. Baruch Schieber
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  3. Michal Ziv-Ukelson
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Editor information

Editors and Affiliations

  1. Depto. de Ciencias de la Computación, Universidad de Chile, Blanco Encalada 2120, Santiago, 6511224, Chile

    Ricardo Baeza-Yates

  2. Escuela de Ciencias Físico-Matemáticas, Universidad Michoacana, Edificio “B”, ciudad universitaria, Morelia Michoacán, Mexico

    Edgar Chávez

  3. Université de Marne-la-Vallée, 77454, Marne-la-Vallée Cedex 2, France

    Maxime Crochemore

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© 2003 Springer-Verlag Berlin Heidelberg

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Landau, G.M., Schieber, B., Ziv-Ukelson, M. (2003). Sparse LCS Common Substring Alignment. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds) Combinatorial Pattern Matching. CPM 2003. Lecture Notes in Computer Science, vol 2676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44888-8_17

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  • DOI: https://doi.org/10.1007/3-540-44888-8_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40311-1

  • Online ISBN: 978-3-540-44888-4

  • eBook Packages: Springer Book Archive

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