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

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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. 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.

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Akutsu, T., Tamura, T., Melkman, A. A., & Takasu, A. (2015). On the complexity of finding a largest common subtree of bounded degree. Theoretical Computer Science, 590, 2–16. https://doi.org/10.1016/j.tcs.2014.10.012

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