On the Approximation of Shortest Common Supersequencesand Longest Common Subsequences
SIAM Journal on Computing
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
Some APX-completeness results for cubic graphs
Theoretical Computer Science
Introduction to Algorithms
The Longest Common Subsequence Problem for Small Alphabet Size Between Many Strings
ISAAC '92 Proceedings of the Third International Symposium on Algorithms and Computation
A polyhedral investigation of the LCS problem and a repetition-free variant
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Repetition-free longest common subsequence
Discrete Applied Mathematics
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In the paper we investigate the computational and approximation complexity of the Exemplar Longest Common Subsequence of a set of sequences (ELCS problem), a generalization of the Longest Common Subsequence problem, where the input sequences are over the union of two disjoint sets of symbols, a set of mandatory symbols and a set of optional symbols. We show that different versions of the problem are APX-hard even for instances with two sequences. Moreover, we show that the related problem of determining the existence of a feasible solution of the Exemplar Longest Common Subsequence of two sequences is NP-hard. On the positive side, efficient algorithms for the ELCS problem over instances of two sequences where each mandatory symbol can appear totally at most three times or the number of mandatory symbols is bounded by a constant are given.