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

Authors:
Carlos E. R. Alves;Edson N. Caceres;Siang Wun Song
Affiliations:
Faculdade de Tecnologia e Ciencias Exatas, Universidade Sao Judas Tadeu, Sao Paulo, SP, Brazil;Universidade Fed. de Mato Grosso do Sul, Campo Grande, MS, Brazil;Universidade de Sao Paulo, Sao Paulo, SP, Brazil
Venue:
Algorithmica
Year:
2006

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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 a 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.