An Improved Approximation Algorithm for the Hard Uniform Capacitated k-median Problem

In the k-median problem, given a set of locations, the goal is to select a subset of at most k centers so as to minimize the total cost of connecting each location to its nearest center. We study the uniform hard capacitated version of the k-median problem, in which each selected center can only serve a limited number of locations. Inspired by the algorithm of Charikar, Guha, Tardos and Shmoys, we give a (6 + 10α)approximation algorithm for this problem with increasing the capacities by a factor of 2+ 2 α , α ≥ 4, which improves the previous best (32l+28l+7)-approximation algorithm proposed by Byrka, Fleszar, Rybicki and Spoerhase violating the capacities by factor 2 + 3 l−1 , l ∈ {2, 3, 4, . . . }.