The parameterized complexity of sequence alignment and consensus
Theoretical Computer Science
On the efficiency of polynomial time approximation schemes
Information Processing Letters
An integrated complexity analysis of problems from computational biology
An integrated complexity analysis of problems from computational biology
Finding similar regions in many strings
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Distinguishing string selection problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for phylogenetic footprinting
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
Combinatorial Approaches to Finding Subtle Signals in DNA Sequences
Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
Exact Solutions for CLOSEST STRING and Related Problems
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Spelling Approximate Repeated or Common Motifs Using a Suffix Tree
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
A Polynominal Time Approximation Scheme for the Closest Substring Problem
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
On the complexity of finding common approximate substrings
Theoretical Computer Science
Hard problems in similarity searching
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
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
Hard problems in similarity searching
Discrete Applied Mathematics
Complexities of the centre and median string problems
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
A lower bound on approximation algorithms for the closest substring problem
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
On the hardness of counting and sampling center strings
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
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
On the Hardness of Counting and Sampling Center Strings
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We show that CLOSEST SUBSTRING, one of the most important problems in the field of biological sequence analysis, is W[1]-hard with respect to the number k of input strings (even over a binary alphabet). This problem is therefore unlikely to be solvable in time O(f(k)nc) for any function f and constant c independent of k -- effectively, the problem can be expected to be intractable, in any practical sense, for k 驴 3. Our result supports the intuition that CLOSEST SUBSTRING is computationally much harder than the special case of CLOSEST STRING, although both problems are NP-complete and both possess polynomial time approximation schemes. We also prove W[1]-hardness for other parameterizations in the case of unbounded alphabet size. Our main W[1]- hardness result generalizes to CONSENSUS PATTERNS, a problem of similar significance in computational biology.