Parallel Algorithms for the Longest Common Subsequence Problem

  • Authors:
  • M. Lu;H. Lin

  • Affiliations:
  • -;-

  • Venue:
  • IEEE Transactions on Parallel and Distributed Systems
  • Year:
  • 1994

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Abstract

A subsequence of a given string is any string obtained by deleting none or some symbolsfrom the given string. A longest common subsequence (LCS) of two strings is a commonsubsequence of both that is as long as any other common subsequences. The problem isto find the LCS of two given strings. The bound on the complexity of this problem underthe decision tree model is known to be mn if the number of distinct symbols that canappear in strings is infinite, where m and n are the lengths of the two strings,respectively, and m/spl les/n. In this paper, we propose two parallel algorithms far thisproblem on the CREW-PRAM model. One takes O(log/sup 2/m + log n) time with mn/log m processors, which is faster than all the existing algorithms on the same model. The other takes O(log/sup 2/m log log m) time with mn/(log/sup 2/m log log m) processors when log/sup 2/m log log m