Information Processing Letters
The spatial complexity of oblivious k-probe Hash functions
SIAM Journal on Computing
Fast linear-space computations of longest common subsequences
Theoretical Computer Science - Selected papers of the Combinatorial Pattern Matching School
Journal of the ACM (JACM)
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)
Introduction to Algorithms
MFCS '94 Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science 1994
A Survey of Longest Common Subsequence Algorithms
SPIRE '00 Proceedings of the Seventh International Symposium on String Processing Information Retrieval (SPIRE'00)
The constrained longest common subsequence problem
Information Processing Letters
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
A simple algorithm for the constrained sequence problems
Information Processing Letters
Exemplar Longest Common Subsequence
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Constrained LCS: Hardness and Approximation
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
A polyhedral investigation of the LCS problem and a repetition-free variant
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
On the parameterized complexity of the repetition free longest common subsequence problem
Information Processing Letters
Approximability of constrained LCS
Journal of Computer and System Sciences
Doubly-Constrained LCS and Hybrid-Constrained LCS problems revisited
Information Processing Letters
The constrained shortest common supersequence problem
Journal of Discrete Algorithms
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We consider a variant of the classical Longest Common Subsequence problem called Doubly-Constrained Longest Common Subsequence (DC-LCS). Given two strings s"1 and s"2 over an alphabet @S, a set C"s of strings, and a function C"o:@S-N, the DC-LCS problem consists of finding the longest subsequence s of s"1 and s"2 such that s is a supersequence of all the strings in C"s and such that the number of occurrences in s of each symbol @s@?@S is upper bounded by C"o(@s). The DC-LCS problem provides a clear mathematical formulation of a sequence comparison problem in Computational Biology and generalizes two other constrained variants of the LCS problem that have been introduced previously in the literature: the Constrained LCS and the Repetition-Free LCS. We present two results for the DC-LCS problem. First, we illustrate a fixed-parameter algorithm where the parameter is the length of the solution which is also applicable to the more specialized problems. Second, we prove a parameterized hardness result for the Constrained LCS problem when the parameter is the number of the constraint strings (|C"s|) and the size of the alphabet @S. This hardness result also implies the parameterized hardness of the DC-LCS problem (with the same parameters) and its NP-hardness when the size of the alphabet is constant.