Generalized LCS

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

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

7 Scopus citations

Abstract

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 give, what is to our knowledge, the first inherently multi-dimensional definition of LCS. We discuss the Longest Common Substructure of two matrices and the Longest Common Subtree problem for multiple trees including a constrained version. Both problems cannot be solved by a natural extension of the original LCS solution. We investigate the tractability of the above problems. For the first we prove NP-Conipleteness. For the latter NP-hardness holds for two general unordered trees and for k trees in the constrained LCS.

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 14th International Symposium, SPIRE 2007, Proceedings
PublisherSpringer Verlag
Pages50-61
Number of pages12
ISBN (Print)9783540755296
DOIs
StatePublished - 2007
Event14th International Symposium on String Processing and Information Retrieval, SPIRE 2007 - Santiago, Chile
Duration: 29 Oct 200731 Oct 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4726 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Symposium on String Processing and Information Retrieval, SPIRE 2007
Country/TerritoryChile
CitySantiago
Period29/10/0731/10/07

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.

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