Fast algorithms for computing tree LCS

Shay Mozes, Dekel Tsur, Oren Weimann, Michal Ziv-Ukelson

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


The LCS of two rooted, ordered, and labeled trees F and G is the largest forest that can be obtained from both trees by deleting nodes. We present algorithms for computing tree LCS which exploit the sparsity inherent to the tree LCS problem. Assuming G is smaller than F, our first algorithm runs in time , where r is the number of pairs (v ∈ F, w ∈ G) such that v and w have the same label. Our second algorithm runs in time , where L is the size of the LCS of F and G. For this algorithm we present a novel three dimensional alignment graph. Our third algorithm is intended for the constrained variant of the problem in which only nodes with zero or one children can be deleted. For this case we obtain an time algorithm, where h = height(F) + height(G).

Original languageEnglish
Title of host publicationCombinatorial Pattern Matching - 19th Annual Symposium, CPM 2008, Proceedings
Number of pages14
StatePublished - 2008
Externally publishedYes
Event19th Annual Symposium on Combinatorial Pattern Matching, CPM 2008 - Pisa, Italy
Duration: 18 Jun 200820 Jun 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5029 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th Annual Symposium on Combinatorial Pattern Matching, CPM 2008

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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