An improved integer linear programming formulation for the closest 0-1 string problem

The Closest String Problem (CSP) calls for finding an n-string that minimizes its maximum Hamming distance from m given n-strings. Recently, integer linear programs (ILP) have been successfully applied within heuristics to improve efficiency and effectiveness. We consider an ILP for the binary case (0-1 CSP) that updates the previous formulations and solve it by branch-and-cut. The method separates in polynomial time the first closure of {0,12}-Chvátal-Gomory cuts and can either be used stand-alone to find optimal solutions, or as a plug-in to improve heuristics based on the exact solution of reduced problems. Due to the parity structure of the right-hand side, the impressive performances obtained with this method in the binary case cannot be directly replicated in the general case.