LCS approximation via embedding into local non-repetitive strings

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A classical measure of similarity between strings is the length of the longest common subsequence(LCS) between the two given strings. The search for efficient algorithms for finding the LCS has been going on for more than three decades. To date, all known algorithms may take quadratic time (shaved by logarithmic factors) to find large LCS. In this paper the problem of approximating LCS is studied, while focusing on the hard inputs for this problem, namely, approximating LCS of near-linear size in strings over relatively large alphabet (of size at least n ε for some constant ε> 0, where n is the length of the string). We show that, any given string over relatively large alphabet can be embedded into a local non-repetitive string. This embedding has a negligible additive distortion for strings that are not too dissimilar in terms of the edit distance. We also show that LCS can be efficiently approximated in locally-non-repetitive strings.

Original languageEnglish
Title of host publicationCombinatorial Pattern Matching - 20th Annual Symposium, CPM 2009, Proceedings
Number of pages14
StatePublished - 2009
Event20th Annual Symposium on Combinatorial Pattern Matching, CPM 2009 - Lille, France
Duration: 22 Jun 200924 Jun 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5577 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference20th Annual Symposium on Combinatorial Pattern Matching, CPM 2009

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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