A Simple Algorithm for the Constrained Sequence Problems
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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 <cit.> proposed an O(n^2 · m^2 · 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.
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