The Closest Substring problem with small distances
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
An improved lower bound on approximation algorithms for the Closest Substring problem
Information Processing Letters
On the Structure of Small Motif Recognition Instances
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
Efficient Algorithms for the Closest String and Distinguishing String Selection Problems
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
More efficient algorithms for closest string and substring problems
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
A three-string approach to the closest string problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
On the hardness of counting and sampling center strings
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
More Efficient Algorithms for Closest String and Substring Problems
SIAM Journal on Computing
The bounded search tree algorithm for the closest string problem has quadratic smoothed complexity
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
A three-string approach to the closest string problem
Journal of Computer and System Sciences
Finding maximum colorful subtrees in practice
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
On the Hardness of Counting and Sampling Center Strings
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
On approximating string selection problems with outliers
Theoretical Computer Science
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We show that Closest Substring, one of the most important problems in the field of consensus string analysis, is W[1]-hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This is done by giving a “strongly structure-preserving” reduction from the graph problem Clique to Closest Substring. This problem is therefore unlikely to be solvable in time O(f(k)•nc) for any function f of k and constant c independent of k, i.e., the combinatorial explosion seemingly inherent to this NP-hard problem cannot be restricted to parameter k. The problem can therefore be expected to be intractable, in any practical sense, for k ≥ 3. Our result supports the intuition that Closest Substring is computationally much harder than the special case of Closest String, althoughb othp roblems are NP-complete. We also prove W[1]-hardness for other parameterizations in the case of unbounded alphabet size. Our W[1]-hardness result for Closest Substring generalizes to Consensus Patterns, a problem arising in computational biology.