AN EFFICIENT ALGORITHM FOR THE CLOSEST STRING PROBLEM

Abstract

The closest string problem that arises in computational molecular biology and coding theory is to find a string that minimizes the maximum Hamming distance from a given set of strings, the CSP is NP-hard problem. This article proposes an efficient algorithm for this problem with three strings. The key idea is to apply normalization for the CSP instance. This enables us to decompose the problem in five different cases corresponding to each position of the strings. Furthermore, an optimal solution can be easily obtained in linear time. A formal proof of the algorithm will be presented, also numerical experiments will show the effectiveness of the proposed algorithm.