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

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

doi:10.1016/j.tcs.2014.10.012

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

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

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

5 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. The 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 present an O((H2{dot operator}22H-1{dot operator}D2H)D-1poly(n)) time algorithm, where H is the maximum height of two input trees.

Original language	English
Pages (from-to)	2-16
Number of pages	15
Journal	Theoretical Computer Science
Volume	590
DOIs	https://doi.org/10.1016/j.tcs.2014.10.012
State	Published - 26 Jul 2015

Keywords

Dynamic programming
Parameterized complexity
Tree edit distance
Unordered trees

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1016/j.tcs.2014.10.012

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title = "On the complexity of finding a largest common subtree of bounded degree",

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. The 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 present an O((H2\{dot operator\}22H-1\{dot operator\}D2H)D-1poly(n)) time algorithm, where H is the maximum height of two input trees.",

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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AU - Akutsu, Tatsuya

AU - Tamura, Takeyuki

AU - Melkman, Avraham A.

AU - Takasu, Atsuhiro

PY - 2015/7/26

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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. The 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 present an O((H2{dot operator}22H-1{dot operator}D2H)D-1poly(n)) time algorithm, where H is the maximum height of two input trees.

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. The 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 present an O((H2{dot operator}22H-1{dot operator}D2H)D-1poly(n)) time algorithm, where H is the maximum height of two input trees.

KW - Dynamic programming

KW - Parameterized complexity

KW - Tree edit distance

KW - Unordered trees

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JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -

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

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Keywords

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