A simple algorithm for the constrained sequence problems

Authors:
Francis Y. L. Chin;Alfredo De Santis;Anna Lisa Ferrara;N. L. Ho;S. K. Kim
Affiliations:
Department of Computer Science and Information Systems, The University of Hong Kong, Pokfulam Road, Hong Kong;Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081 Baronissi (SA), Italy;Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081 Baronissi (SA), Italy;Department of Computer Science and Information Systems, The University of Hong Kong, Pokfulam Road, Hong Kong;Department of Computer Science and Engineering, Chung-Ang University, 221 Huksuk-dong, Dongjak-ku, Seoul 156-756, Republic of Korea
Venue:
Information Processing Letters
Year:
2004

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Abstract

In this paper we address the constrained longest common subsequence problem. Given two sequences X, Y and a constrained sequence P, a sequence Z is a constrained longest common subsequence for X and Y with respect to P if Z is the longest subsequence of X and Y such that P is a subsequence of Z.Recently, Tsai [Inform. Process. Lett. 88 (2003) 173-176] proposed an O(n2 . m2 . r) time algorithm to solve this problem using dynamic programming technique, where n, m and r are the lengths of X, Y and P, respectively.In this paper, we present a simple algorithm to solve the constrained longest common subsequence problem in O(n . m . r) time and show that the constrained longest common subsequence problem is equivalent to a special case of the constrained multiple sequence alignment problem which can also be solved with the same time complexity.