Why Large Closest String Instances Are Easy to Solve in Practice

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Why Large Closest String Instances Are Easy to Solve in Practice
We initiate the study of the smoothed complexity of the Closest String problem by proposing a semi-random model of Hamming distance. We restrict interest to the optimization version of the Closest String problem and give a randomized algorithm, we refer to as CSP-Greedy, that computes the closest string on smoothed instances up to a constant factor approximation in time O( 3 ), where is the string length. Using smoothed analysis, we prove CSP-Greedy achieves a ` (1 + e 2n ) ´ -approximation guarantee, where > 0 is any small value and n is the number of strings. These approximation and runtime guarantees demonstrate that Closest String instances with a relatively large number of input strings are efficiently solved in practice. We also give experimental results demonstrating that CSP-greedy runs extremely efficiently on instances with a large number of strings. This counter-intuitive fact that “large” Closest String instances are easier and more efficient to solve gives new insi...
Christina Boucher, Kathleen Wilkie
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Authors Christina Boucher, Kathleen Wilkie
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