A three-string approach to the closest string problem

Abstract

Given a set of n strings of length L and a radius d, the closest string problem asks for a new string t sol that is within a Hamming distance of d to each of the given strings. It is known that the problem is NP-hard and its optimization version admits a polynomial time approximation scheme (PTAS). Parameterized algorithms have been then developed to solve the problem when d is small. In this paper, with a new approach (called the 3-string approach), we first design a parameterized algorithm for binary strings that runs in time, while the previous best runs in time. We then extend the algorithm to arbitrary alphabet sizes, obtaining an algorithm that runs in time, where . This new time bound is better than the previous best for small alphabets, including the very important case where |∑|=4 (i.e., the case of DNA strings). © 2010 Springer-Verlag Berlin Heidelberg.