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Alignment of trees — An alternative to tree edit

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Combinatorial Pattern Matching (CPM 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 807))

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Abstract

In this paper, we propose the alignment of trees as a measure of the similarity between two labeled trees. Both ordered and unordered trees are considered. An algorithm is designed for ordered trees. The time complexity of this algorithm is O(¦T 1¦· s¦T 2· (deg(T 1) + deg(T 2))2), where ¦T i¦ is the number of nodes in T i and deg(T i ) is the degree of T i , i=1,2. The algorithm is faster than the best known algorithm for tree edit when deg(T 1) and deg(T 2) are smaller than the depths of T 1 and T 2. For unordered trees, we show that the alignment problem can be solved in polynomial time if the trees have a bounded degree and becomes NP-hard if one of the trees is allowed to have an arbitrary degree. In contrast, the edit problem for unordered trees is NP-hard even if both trees have a bounded degree [17]. Finally, multiple alignment of trees is discussed.

Supported in part by NSERC Research Grant OGP0046613.

Supported in part by NSERC Research Grant OGP0046373.

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Author information

Authors and Affiliations

  1. Department of Computer Science, McMaster University, L8S 4K1, Hamilton, Ont., Canada

    Tao Jiang

  2. Department of Electrical and Computer Engineering, McMaster University, L8S 4K1, Hamilton, Ont., Canada

    Lusheng Wang

  3. Department of Computer Science, University of Western Ontario, N6A 5B7, London, Ont., Canada

    Kaizhong Zhang

Authors
  1. Tao Jiang
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  2. Lusheng Wang
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  3. Kaizhong Zhang
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Editor information

Maxime Crochemore Dan Gusfield

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© 1994 Springer-Verlag Berlin Heidelberg

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Jiang, T., Wang, L., Zhang, K. (1994). Alignment of trees — An alternative to tree edit. In: Crochemore, M., Gusfield, D. (eds) Combinatorial Pattern Matching. CPM 1994. Lecture Notes in Computer Science, vol 807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58094-8_7

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  • DOI: https://doi.org/10.1007/3-540-58094-8_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58094-2

  • Online ISBN: 978-3-540-48450-9

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