Efficient polynomial-time algorithms for the constrained LCS problem with strings exclusion

Hsing-Yen Ann, Chang-Biau Yang () and Chiou-Ting Tseng
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Hsing-Yen Ann: National Center for High-Performance Computing
Chang-Biau Yang: National Sun Yat-sen University
Chiou-Ting Tseng: National Sun Yat-sen University

Journal of Combinatorial Optimization, 2014, vol. 28, issue 4, No 7, 800-813

Abstract: Abstract In this paper, we revisit a recent variant of the longest common subsequence (LCS) problem, the string-excluding constrained LCS (STR-EC-LCS) problem, which was first addressed by Chen and Chao (J Comb Optim 21(3):383–392, 2011). Given two sequences $$X$$ and $$Y$$ of lengths $$m$$ and $$n,$$ respectively, and a constraint string $$P$$ of length $$r,$$ we are to find a common subsequence $$Z$$ of $$X$$ and $$Y$$ which excludes $$P$$ as a substring and the length of $$Z$$ is maximized. In fact, this problem cannot be correctly solved by the previously proposed algorithm. Thus, we give a correct algorithm with $$O(mnr)$$ time to solve it. Then, we revisit the STR-EC-LCS problem with multiple constraints $$\{ P_1, P_2, \ldots , P_k \}.$$ We propose a polynomial-time algorithm which runs in $$O(mnR)$$ time, where $$R = \sum _{i=1}^{k} |P_i|,$$ and thus it overthrows the previous claim of NP-hardness.

Keywords: Design of algorithms; Longest common subsequence; Constrained LCS; NP-hard; Finite automata (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-012-9588-2

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