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Bit-Parallel Branch and Bound Algorithm for Transposition Invariant LCS

  • Conference paper
String Processing and Information Retrieval (SPIRE 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3246))

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Abstract

We consider the problem of longest common subsequence (LCS) of two given strings in the case where the first may be shifted by some constant (i.e. transposed) to match the second. For this longest common transposition invariant subsequence (LCTS) problem, that has applications for instance in music comparison, we develop a branch and bound algorithm with best case time O((m 2 + loglog σ) logσ) and worst case time O((m 2 + log σ) σ), where m and σ are the length of the strings and the number of possible transpositions, respectively. This compares favorably against the O(σm 2) naive algorithm in most cases and, for large m, against the O(m 2loglog m) time algorithm of [2].

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References

  1. Lemström, K., Navarro, G.: Flexible and efficient bit-parallel techniques for transposition invariant approximate matching in music retrieval. In: Nascimento, M.A., de Moura, E.S., Oliveira, A.L. (eds.) SPIRE 2003. LNCS, vol. 2857, pp. 224–237. Springer, Heidelberg (2003)

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  2. Mäkinen, V., Navarro, G., Ukkonen, E.: Algorithms for transposition invariant string matching. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 191–202. Springer, Heidelberg (2003)

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Helsinki, Finland

    Kjell Lemström

  2. Department of Computer Science, University of Chile,  

    Gonzalo Navarro

  3. Department of Computer Science, King’s College, London, UK

    Yoan Pinzon

  4. Department of computer Science, Autonomous University of Bucaramanga, Colombia

    Yoan Pinzon

Authors
  1. Kjell Lemström
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  2. Gonzalo Navarro
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  3. Yoan Pinzon
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Editor information

Editors and Affiliations

  1. Georgia Institute of Technology and Università di Padova,  

    Alberto Apostolico

  2. Department of Information Engineering, University of Padova,  

    Massimo Melucci

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© 2004 Springer-Verlag Berlin Heidelberg

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Lemström, K., Navarro, G., Pinzon, Y. (2004). Bit-Parallel Branch and Bound Algorithm for Transposition Invariant LCS. In: Apostolico, A., Melucci, M. (eds) String Processing and Information Retrieval. SPIRE 2004. Lecture Notes in Computer Science, vol 3246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30213-1_10

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  • DOI: https://doi.org/10.1007/978-3-540-30213-1_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23210-0

  • Online ISBN: 978-3-540-30213-1

  • eBook Packages: Springer Book Archive

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