Given a set S of n strings, each of length ℓ, and a non-negative 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 + nd·dd )-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 + nd·d2+0(1)). © 2011 Springer-Verlag GmbH.
CITATION STYLE
Boucher, C. (2011). The bounded search tree algorithm for the Closest String problem has quadratic smoothed complexity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6907 LNCS, pp. 158–169). https://doi.org/10.1007/978-3-642-22993-0_17
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