Practical planning: extending the classical AI planning paradigm
Practical planning: extending the classical AI planning paradigm
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
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Introduction to Algorithms
The constrained longest common subsequence problem
Information Processing Letters
A simple algorithm for the constrained sequence problems
Information Processing Letters
BIBE '06 Proceedings of the Sixth IEEE Symposium on BionInformatics and BioEngineering
Exemplar Longest Common Subsequence
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
New efficient algorithms for the LCS and constrained LCS problems
Information Processing Letters
Repetition-free longest common subsequence
Discrete Applied Mathematics
Variants of constrained longest common subsequence
Information Processing Letters
On shortest common superstring and swap permutations
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Restricted common superstring and restricted common supersequence
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Parameterized Complexity
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Shortest common supersequence and longest common subsequence are two widely used measures to compare sequences in different fields, from AI planning to Bioinformatics. Inspired by recently proposed variants of these two measures, we introduce a new version of the shortest common supersequence problem, where the solution is required to satisfy a given constraint on the number of occurrences of each symbol. First, we investigate the computational and approximation complexity of the problem, then we give a 32-approximation algorithm. Finally, we investigate the parameterized complexity of the problem, and we present a fixed-parameter algorithm.