Generalized LCS

Amihood Amir, Tzvika Hartman, Oren Kapah, B. Riva Shalom, Dekel Tsur

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The Longest Common Subsequence (LCS) is a well studied problem, having a wide range of implementations. Its motivation is in comparing strings. It has long been of interest to devise a similar measure for comparing higher dimensional objects, and more complex structures. In this paper we study the Longest Common Substructure of two matrices and show that this problem is N P-hard. We also study the Longest Common Subforest problem for multiple trees including a constrained version, as well. We show N P-hardness for k > 2 unordered trees in the constrained LCS. We also give polynomial time algorithms for ordered trees and prove a lower bound for any decomposition strategy for k trees.

Original languageEnglish
Pages (from-to)438-449
Number of pages12
JournalTheoretical Computer Science
Issue number3
StatePublished - 28 Dec 2008

Bibliographical note

Funding Information:
The authors wish to thank the anonymous referees for their helpful comments. The first author was partly supported by ISF grant 35/05.


  • Longest common subsequence
  • Matrices
  • Non crossing matching
  • Trees


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