Matching for run-length encoded strings
Journal of Complexity
Bounds on the Complexity of the Longest Common Subsequence Problem
Journal of the ACM (JACM)
Algorithms for the Longest Common Subsequence Problem
Journal of the ACM (JACM)
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
A linear space algorithm for computing maximal common subsequences
Communications of the ACM
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
A simple algorithm for the constrained sequence problems
Information Processing Letters
New efficient algorithms for the LCS and constrained LCS problems
Information Processing Letters
Constrained LCS: Hardness and Approximation
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
On the generalized constrained longest common subsequence problems
Journal of Combinatorial Optimization
Finite automata based algorithms for the generalized constrained longest common subsequence problems
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
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The Longest Common Subsequence (LCS) of two or more strings is a fundamental well-studied problem which has a wide range of applications throughout computational sciences. When the common subsequence must contain one or more constraint strings as subsequences, the problem becomes the Constrained LCS (CLCS) problem. In this paper we consider the Restricted LCS (RLCS) problem, where our goal is finding a longest common subsequence between two or more strings that does not contain a given set of restriction strings as subsequences. First we show that in case of two input strings and an arbitrary number of restriction strings the RLCS problem is NP-hard. Afterwards, we present a dynamic programming solution for RLCS and we show that this algorithm implies that RLCS is in FPT when parameterized by the total length of the restriction strings. In the last part of this paper we present two approximation algorithms for the hard variants of the problem.