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The Longest Common Subsequence Problem A Finite Automata Approach

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Implementation and Application of Automata (CIAA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2759))

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Abstract

A new algorithm that creates a common subsequence automaton for a set of strings is presented. Moreover, it is shown that a longest common subsequence of two strings over a constant alphabet can be found in \( \mathcal{O}\left( {\left| A \right|\left( {\left| {S_1 } \right| + \left| {S_2 } \right| + \sum _{\alpha \in A} \left| {S_1 } \right|_\alpha \left| {S_2 } \right|_\alpha } \right)} \right) \) time, where |A| is the size of the alphabet, |S i | is the length of the input string i, and |S i |a is the number of occurrences of a ∈ A in S i .

This research has been partialy supported by the Ministry of Education, Youth, and Sports of the Czech Republic under research program No. J04/98:212300014 (Research in the area of information technologies and cummunications) and by Grant Agency of Czech Republic grant No. 201/01/1433.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering Faculty of Electrical Engineering, Czech Technical University, Karlovo nám. 13, 121 35, Prague 2, Czech Republic

    Bořivoj Melichar & Tomáš Polcar

Authors
  1. Bořivoj Melichar
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  2. Tomáš Polcar
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

  2. School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA, 99163, USA

    Zhe Dang

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© 2003 Springer-Verlag Berlin Heidelberg

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Melichar, B., Polcar, T. (2003). The Longest Common Subsequence Problem A Finite Automata Approach. In: Ibarra, O.H., Dang, Z. (eds) Implementation and Application of Automata. CIAA 2003. Lecture Notes in Computer Science, vol 2759. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45089-0_27

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  • DOI: https://doi.org/10.1007/3-540-45089-0_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40561-0

  • Online ISBN: 978-3-540-45089-4

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