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All semi-local longest common subsequences in subquadratic time
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Tiskin, Alexander (2006) All semi-local longest common subsequences in subquadratic time. In: Grigoriev, D. and Harrison, J. and Hirsch, E. A., (eds.) Computer Science – Theory and Applications. Lecture Notes in Computer Science, Volume 3967 . Springer Berlin Heidelberg, pp. 352-363. ISBN 9783540341666
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Official URL: http://dx.doi.org/10.1007/11753728_36
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 Theta((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. 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: | Book Item | ||||
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Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
Series Name: | Lecture Notes in Computer Science | ||||
Publisher: | Springer Berlin Heidelberg | ||||
ISBN: | 9783540341666 | ||||
ISSN: | 0302-9743 | ||||
Book Title: | Computer Science – Theory and Applications | ||||
Editor: | Grigoriev, D. and Harrison, J. and Hirsch, E. A. | ||||
Official Date: | 2006 | ||||
Dates: |
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Volume: | Volume 3967 | ||||
Number of Pages: | 12 | ||||
Page Range: | pp. 352-363 | ||||
DOI: | 10.1007/11753728_36 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 15 December 2015 | ||||
Conference Paper Type: | Paper | ||||
Title of Event: | International Computer Science Symposium in Russia (CSR 2006) | ||||
Type of Event: | Conference | ||||
Location of Event: | Steklov Inst Math, St Petersburg, Russia | ||||
Date(s) of Event: | 08-12 Jun 2006 | ||||
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