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 an improved approximation algorithm for this problem with increasing the capacities by a constant factor, which improves the previous best approximation algorithm proposed by Byrka, Fleszar, Rybicki and Spoerhase