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Algorithms 2013, 6(3), 485-493; doi:10.3390/a6030485

A Simple Algorithm for Solving for the Generalized Longest Common Subsequence (LCS) Problem with a Substring Exclusion Constraint

1
Faculty of Mathematics & Computer Science, Quanzhou Normal University, Quanzhou 362000, China
2
Faculty of Mathematics & Computer Science, Fuzhou University, Fuzhou 350108, China
*
Author to whom correspondence should be addressed.
Received: 14 June 2013 / Revised: 15 July 2013 / Accepted: 24 July 2013 / Published: 15 August 2013
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Abstract

This paper studies the string-excluding (STR-EC)-constrained longest common subsequence (LCS) problem, a generalized LCS problem. For the two input sequences, X and Y , of lengths n andmand a constraint string, P, of length r, the goal is to find the longest common subsequence, Z, of X and Y that excludes P as a substring. The problem and its solution were first proposed by Chen and Chao, but we found that their algorithm cannot solve the problem correctly. A new dynamic programming solution for the STR-EC-LCS problem is then presented in this paper, and the correctness of the new algorithm is proven. The time complexity of the new algorithm is O(nmr). View Full-Text
Keywords: constrained LCS; string-excluding; dynamic programming constrained LCS; string-excluding; dynamic programming
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Zhu, D.; Wang, X. A Simple Algorithm for Solving for the Generalized Longest Common Subsequence (LCS) Problem with a Substring Exclusion Constraint. Algorithms 2013, 6, 485-493.

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