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

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.