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
Banishing Bias from Consensus Sequences
CPM '97 Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching
On the Parameterized Intractability of CLOSEST SUBSTRINGsize and Related Problems
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Distinguishing string selection problems
Information and Computation
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
On the Optimality of the Dimensionality Reduction Method
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Smoothed analysis of binary search trees
Theoretical Computer Science
Why Greed Works for Shortest Common Superstring Problem
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
The Smoothed Complexity of Edit Distance
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Efficient Algorithms for the Closest String and Distinguishing String Selection Problems
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Exact Solutions for Closest String and Related Problems
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
A three-string approach to the closest string problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
More Efficient Algorithms for Closest String and Substring Problems
SIAM Journal on Computing
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Parameterized Complexity
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Given a set S of n strings, each of length l, and a nonnegative value d, we define a center string as a string of length l that has Hamming distance at most d from each string in S. The Closest String problem aims to determine whether there exists a center string for a given set of strings S and input parameters n, l, and d. When n is relatively large with respect to l then the basic majority algorithm solves the CLOSEST STRING problem efficiently, and the problem can also be solved efficiently when either n, l or d is reasonably small [12]. Hence, the only case for which there is no known efficient algorithm is when n is between log l/ log log l and log l. Using smoothed analysis, we prove that such CLOSEST STRING instances can be solved efficiently by the O(nl + ndċdd)-time algorithm by Gramm et al. [13]. In particular, we show that for any given CLOSEST STRING instance I, the expected running time of this algorithm on a small perturbation of I is O(nl + ndċd2+o(1)).