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Algorithmica

, Volume 45, Issue 3, pp 301–335 | Cite as

A Coarse-Grained Parallel Algorithm for the All-Substrings Longest Common Subsequence Problem

  • Carlos E.R. Alves
  • Edson N. Caceres
  • Siang Wun Song
Article

Abstract

Given two strings A and B of lengths na and nb, respectively, the All-substrings Longest Common Subsequence (ALCS) problem obtains, for any substring B' of B, the length of the longest string that is a subsequence of both A and B'. The sequential algorithm for this problem takes O(na nb) time and O(nb) space. We present a parallel algorithm for the ALCS problem on the Coarse-Grained Multicomputer (BSP/CGM) model with p < √na processors, that takes O(na nb/p) time, O(log p) communication rounds and O(nb √na) space per processor. The proposed algorithm also solves the basic Longest Common Subsequence (LCS) problem that finds the longest string (and not only its length) that is a subsequence of both A and B. To our knowledge, this is the best BSP/CGM algorithm in the literature for the LCS and ALCS problems.

Keywords

Sequential Algorithm Longe Common Subsequence Longe Common Subsequence Communication Round Bulk Synchronous Parallel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Faculdade de Tecnologia e Ciencias Exatas, Universidade Sao Judas Tadeu, Sao Paulo, SPBrazil
  2. 2.Universidade Fed. de Mato Grosso do Sul, Campo Grande, MSBrazil
  3. 3.Universidade de Sao Paulo, Sao Paulo, SPBrazil

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