An optimal decomposition algorithm for tree edit distance

Erik D. Demaine, Shay Mozes, Benjamin Rossman, Oren Weimann

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The edit distance between two ordered rooted trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this paper, we present a worst-case O(n 3)-time algorithm for this problem, improving the previous best O(n3 log n)-time algorithm [7]. Our result requires a novel adaptive strategy for deciding how a dynamic program divides into subproblems, together with a deeper understanding of the previous algorithms for the problem. We prove the optimality of our algorithm among the family of decomposition strategy algorithms-which also includes the previous fastest algorithms-by tightening the known lower bound of Q(n2 log2 n) [4] to Ωn 3), matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds of ⊖(nm2(1 + log m/n)) when the two trees have sizes m and n where m < n.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540734198, 9783540734192
StatePublished - 2007
Externally publishedYes
Event34th International Colloquium on Automata, Languages and Programming, ICALP 2007 - Wroclaw, Poland
Duration: 9 Jul 200713 Jul 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4596 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference34th International Colloquium on Automata, Languages and Programming, ICALP 2007

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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