Efficient exponential-time algorithms for edit distance between unordered trees

Authors:
Tatsuya Akutsu;Takeyuki Tamura;Daiji Fukagawa;Atsuhiro Takasu
Affiliations:
Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan;Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan;Faculty of Culture and Information Science, Doshisha University, Kyoto 610-0394, Japan;National Institute of Informatics, Tokyo 101-8430, Japan
Venue:
Journal of Discrete Algorithms
Year:
2014

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Abstract

The edit distance problem for rooted unordered trees is known to be NP-hard. Based on this fact, this paper studies exponential-time algorithms for the problem. For a general case, an O(min(1.26^n^"^1^+^n^"^2,2^b^"^1^+^b^"^2@?poly(n"1,n"2))) time algorithm is presented, where n"1 and n"2 are the numbers of nodes and b"1 and b"2 are the numbers of branching nodes in two input trees. This algorithm is obtained by a combination of dynamic programming, exhaustive search, and maximum weighted bipartite matching. For bounded degree trees over a fixed alphabet, it is shown that the problem can be solved in O((1+@e)^n^"^1^+^n^"^2) time for any fixed @e0. This result is achieved by avoiding duplicate calculations for identical subsets of small subtrees.