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

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

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)2-16
Number of pages15
JournalTheoretical Computer Science
StatePublished - 26 Jul 2015


  • Dynamic programming
  • Parameterized complexity
  • Tree edit distance
  • Unordered trees


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