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Efficient Exponential Time Algorithms for Edit Distance between Unordered Trees

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Combinatorial Pattern Matching (CPM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7354))

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Abstract

This paper presents efficient exponential time algorithms for the unordered tree edit distance problem, which is known to be NP-hard. For a general case, an \(O(1.26^{n_1+n_2})\) time algorithm is presented, where n 1 and n 2 are the numbers of nodes in two input trees. This algorithm is obtained by a combination of dynamic programming, exhaustive search, and maximum weighted bipartite matching. For bounded degree trees over a fixed alphabet, it is shown that the problem can be solved in \(O((1+\epsilon)^{n_1+n_2})\) time for any fixed ε > 0. This result is achieved by avoiding duplicate calculations for identical subsets of small subtrees.

This work was partially supported by the Collaborative Research Programs of Institute for Chemical Research, Kyoto University and National Institute of Informatics. T.A. and T.T. were partially supported by JSPS, Japan: Grant-in-Aid 22650045 and Grant-in-Aid 23700017, respectively.

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Author information

Authors and Affiliations

  1. Bioinformatics Center, Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto, 611-0011, Japan

    Tatsuya Akutsu & Takeyuki Tamura

  2. Faculty of Culture and Information Science, Doshisha University, Kyoto, 610-0394, Japan

    Daiji Fukagawa

  3. National Institute of Informatics, Tokyo, 101-8430, Japan

    Atsuhiro Takasu

Authors
  1. Tatsuya Akutsu
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  2. Takeyuki Tamura
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  3. Daiji Fukagawa
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  4. Atsuhiro Takasu
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Editors and Affiliations

  1. Department of Computer Science, University of Helsinki, Gustaf Hällström Katu 2b, P.O. Box 68, 00014, Helsinki, Finland

    Juha Kärkkäinen

  2. Faculty of Technology, University of Bielefeld, Universitätsstraße 25, 33615, Bielefeld, Germany

    Jens Stoye

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Akutsu, T., Tamura, T., Fukagawa, D., Takasu, A. (2012). Efficient Exponential Time Algorithms for Edit Distance between Unordered Trees. In: Kärkkäinen, J., Stoye, J. (eds) Combinatorial Pattern Matching. CPM 2012. Lecture Notes in Computer Science, vol 7354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31265-6_29

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  • DOI: https://doi.org/10.1007/978-3-642-31265-6_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31264-9

  • Online ISBN: 978-3-642-31265-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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