On the complexity of finding a largest common subtree of bounded degree

Tatsuya Akutsu; Takeyuki Tamura; Avraham A. Melkman; Atsuhiro Takasu

doi:10.1007/978-3-642-40164-0_4

On the complexity of finding a largest common subtree of bounded degree

Tatsuya Akutsu
, Takeyuki Tamura
, Avraham A. Melkman
, Atsuhiro Takasu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

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.

Original language	English
Title of host publication	Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings
Pages	4-15
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-40164-0_4
State	Published - 3 Sep 2013
Event	19th International Symposium on Fundamentals of Computation Theory, FCT 2013 - Liverpool, United Kingdom Duration: 19 Aug 2013 → 21 Aug 2013

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8070 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	19th International Symposium on Fundamentals of Computation Theory, FCT 2013
Country/Territory	United Kingdom
City	Liverpool
Period	19/08/13 → 21/08/13

Keywords

dynamic programming
parameterized complexity
tree edit distance
unordered trees

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-40164-0_4

Cite this

Akutsu, T., Tamura, T., Melkman, A. A., & Takasu, A. (2013). On the complexity of finding a largest common subtree of bounded degree. In Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings (pp. 4-15). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8070 LNCS). https://doi.org/10.1007/978-3-642-40164-0_4

Akutsu, Tatsuya ; Tamura, Takeyuki ; Melkman, Avraham A. et al. / On the complexity of finding a largest common subtree of bounded degree. Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings. 2013. pp. 4-15 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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(nD) time algorithm where n is the maximum size of two input trees, which improves a previous O(n2D) time algorithm. We also prove that this restricted problem is W[1]-hard for parameter D.",

keywords = "dynamic programming, parameterized complexity, tree edit distance, unordered trees",

author = "Tatsuya Akutsu and Takeyuki Tamura and Melkman, \{Avraham A.\} and Atsuhiro Takasu",

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Akutsu, T, Tamura, T, Melkman, AA & Takasu, A 2013, On the complexity of finding a largest common subtree of bounded degree. in Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8070 LNCS, pp. 4-15, 19th International Symposium on Fundamentals of Computation Theory, FCT 2013, Liverpool, United Kingdom, 19/08/13. https://doi.org/10.1007/978-3-642-40164-0_4

On the complexity of finding a largest common subtree of bounded degree. / Akutsu, Tatsuya; Tamura, Takeyuki; Melkman, Avraham A. et al.
Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings. 2013. p. 4-15 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8070 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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(nD) time algorithm where n is the maximum size of two input trees, which improves a previous O(n2D) time algorithm. We also prove that this restricted problem is W[1]-hard for parameter D.

AB - 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(nD) time algorithm where n is the maximum size of two input trees, which improves a previous O(n2D) time algorithm. We also prove that this restricted problem is W[1]-hard for parameter D.

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KW - parameterized complexity

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Akutsu T, Tamura T, Melkman AA, Takasu A. On the complexity of finding a largest common subtree of bounded degree. In Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Proceedings. 2013. p. 4-15. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-40164-0_4

On the complexity of finding a largest common subtree of bounded degree

Abstract

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Keywords

ASJC Scopus subject areas

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