Distinguishing string selection problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Finding similar regions in many sequences
Journal of Computer and System Sciences - STOC 1999
Combinatorial Approaches to Finding Subtle Signals in DNA Sequences
Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
Parameterized Intractability of Distinguishing Substring Selection
Theory of Computing Systems
Exact Solutions for Closest String and Related Problems
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
New bounds for motif finding in strong instances
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
Sharper upper and lower bounds for an approximation scheme for consensus-pattern
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Long packing and covering codes
IEEE Transactions on Information Theory
Consensus Optimizing Both Distance Sum and Radius
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
Finding optimal alignment and consensus of circular strings
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
A heuristic algorithm based on Lagrangian relaxation for the closest string problem
Computers and Operations Research
Approximations and partial solutions for the consensus sequence problem
SPIRE'11 Proceedings of the 18th international conference on String processing and information retrieval
Enumerating neighbour and closest strings
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Configurations and minority in the string consensus problem
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
Finding consensus and optimal alignment of circular strings
Theoretical Computer Science
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Given a set of sequences, S , and degeneracy parameter, d , the Consensus Sequence problem asks whether there exists a sequence that has Hamming distance at most d from each sequence in S . A valid motif set is a set of sequences for which such a consensus sequence exists, while a decoy set is a set of sequences that does not have a consensus sequence but whose pairwise Hamming distances are all at most 2d . At present, no efficient solution is known to the Consensus Sequence problem when the number of sequences is greater than three. For instances of Consensus Sequence with binary sequences and cardinality four, we present a combinatorial characterization of decoy sets and a linear-time exact algorithm, resolving an open problem posed by Gramm et al. [7].