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

Authors:
Tatsuya Akutsu;Takeyuki Tamura;Avraham A. Melkman;Atsuhiro Takasu
Affiliations:
Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan;Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan;Ben-Gurion University of the Negev, Beer-Sheva, Israel;National Institute of Informatics, Tokyo, Japan
Venue:
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Year:
2013

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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.