Sparse LCS Common Substring Alignment

Gad M. Landau, Baruch Schieber, Michal Ziv-Ukelson

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

7 Scopus citations


The "Common Substring Alignment" problem is defined as follows. The input consists of a set of strings S1,S2...Sc, with a common substring appearing at least once in each of them, and a target string T. The goal is to compute similarity of all strings Si with T, without computing the part of the common substring over and over again. In this paper we consider the Common Substring Alignment problem for the LCS (Longest Common Subsequence) similarity metric. Our algorithm gains its efficiency by exploiting the sparsity inherent to the LCS problem. Let Y be the common substring, n be the size of the compared sequences, Ly be the length of the LCS of T and Y, denoted |LCS[T, Y]|, and L be max{|LCS[T, Si]|}. Our algorithm consists of an O(nLy) time encoding stage that is executed once per common substring, and an O(L) time alignment stage that is executed once for each appearance of the common substring in each source string. The additional running time depends only on the length of the parts of the strings that are not in any common substring.

Original languageEnglish
Title of host publicationCombinatorial Pattern Matching
Subtitle of host publication14th Annual Symposium, CPM 2003
EditorsRicardo Baeza-Yates, Edgar Chavez, Maxime Crochemore
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540403116, 9783540403111
StatePublished - 1 Jan 2003
Externally publishedYes

Publication series

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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