Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
Handbook of combinatorics (vol. 1)
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
Faster exact algorithms for hard problems: a parameterized point of view
Discrete Mathematics
A Linear-Time Algorithm for the 1-Mismatch Problem
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Parameterized Complexity
On the Parameterized Intractability of CLOSEST SUBSTRINGsize and Related Problems
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
An efficient two-phase ant colony optimization algorithm for the closest string problem
SEAL'12 Proceedings of the 9th international conference on Simulated Evolution and Learning
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CLOSEST STRING is one of the core problems in the field of consensus word analysis with particular importance for computational biology. Given k strings of same length and a positive integer d, find a "closest string" s such that none of the given strings has Hamming distance greater than d from s. CLOSEST STRING is NP-complete. We show how to solve CLOSEST STRING in linear time for constant d (the exponential growth is O(dd)). We extend this result to the closely related problems d-MISMATCH AND DISTINGUISHING STRING SELECTION. Moreover, we discuss fixed parameter tractability for parameter k and give an efficient linear time algorithm for Closest STRING when k = 3. Finally, the practical usefulness of our findings is substantiated by some experimental results.