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...

• Type: Journal
• Year: 2010
• Where: SPIRE
• Authors: Christina Boucher, Kathleen Wilkie
• Keywords: Closest String, Closest String Instances, Closest String Problem, Information Technology, SPIRE 2010