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Semi-local longest common subsequences in subquadratic time

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Tiskin, Alexander. (2008) Semi-local longest common subsequences in subquadratic time. Journal of Discrete Algorithms, 6 (4). pp. 570-581. ISSN 1570-8667

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Abstract

For two strings a, b of lengths m, n, respectively, the longest common subsequence (LCS) problem consists in comparing a and b by computing the length of their LCS. In this paper, we define a generalisation, called “the all semi-local LCS problem”, where each string is compared against all substrings of the other string, and all prefixes of each string are compared against all suffixes of the other string. An explicit representation of the output lengths is of size Θ((m+n)2). We show that the output can be represented implicitly by a geometric data structure of size O(m+n), allowing efficient queries of the individual output lengths. The currently best all string–substring LCS algorithm by Alves et al., based on previous work by Schmidt, can be adapted to produce the output in this form. We also develop the first all semi-local LCS algorithm, running in time o(mn) when m and n are reasonably close. Compared to a number of previous results, our approach presents an improvement in algorithm functionality, output representation efficiency, and/or running time.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science > Computer Science
Journal or Publication Title: Journal of Discrete Algorithms
Publisher: Elsevier BV
ISSN: 1570-8667
Date: December 2008
Volume: 6
Number: 4
Page Range: pp. 570-581
Identification Number: 10.1016/j.jda.2008.07.001
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Related URLs:
URI: http://wrap.warwick.ac.uk/id/eprint/47638

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