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On the Complexity of Finding a Largest Common Subtree of Bounded Degree

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Fundamentals of Computation Theory (FCT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8070))

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Abstract

The largest common subtree problem is to find a bijective mapping between subsets of nodes of two input rooted trees of maximum cardinality or weight that preserves labels and ancestry relationship. This problem is known to be NP-hard for unordered trees. In this paper, we consider a restricted unordered case in which the maximum outdegree of a common subtree is bounded by a constant D. We present an O(n D) time algorithm where n is the maximum size of two input trees, which improves a previous O(n 2D) time algorithm. We also prove that this restricted problem is W[1]-hard for parameter D.

This work was partially supported by the Collaborative Research Programs of 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. Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel

    Avraham A. Melkman

  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. Avraham A. Melkman
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  4. Atsuhiro Takasu
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Editor information

Editors and Affiliations

  1. Computer Science, University of Liverpool, Ashton Street, L69 3BX, Liverpool, UK

    Leszek Gąsieniec

  2. Department of Computer Science, University of Liverpool, United Kingdom

    Frank Wolter

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Akutsu, T., Tamura, T., Melkman, A.A., Takasu, A. (2013). On the Complexity of Finding a Largest Common Subtree of Bounded Degree. In: Gąsieniec, L., Wolter, F. (eds) Fundamentals of Computation Theory. FCT 2013. Lecture Notes in Computer Science, vol 8070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40164-0_4

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  • DOI: https://doi.org/10.1007/978-3-642-40164-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40163-3

  • Online ISBN: 978-3-642-40164-0

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