A Three-String Approach to the Closest String Problem

Given a set of n strings of length L and a radius d, the closest string problem (CSP for short) asks for a string tsol 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 O nL + nd3 6.731d time, while the previous best runs in O nL + nd8d time. We then extend the algorithm to arbitrary alphabet sizes, obtaining an algorithm that runs in time

• Type: Conference
• Year: 2010
• Where: COCOON
• Authors: Zhi-Zhong Chen, Bin Ma, Lusheng Wang
• Keywords: Closest String Problem, COCOON 2010, Combinatorics, Parameterized Algorithm, Polynomial Time Approximation Scheme