On Chebyshev radius of a set in Hamming space and the closest string problem

The Chebyshev radius of a set in a metric space is defined to be the radius of the smallest ball containing the set. This quantity is closely related to the covering radius of the set and, in particular for Hamming set, is extensively studied in computational biology. This paper investigates some basic properties of radii of sets in n-dimensional Hamming space, provides a linear programing relaxation and gives tight bounds on the integrality gap. This results in a simple polynomial-time approximation algorithm that attains the performance of the best known such algorithms with shorter running time.