Approximation algorithm for squared metric facility location problem with nonuniform capacities

Abstract

Facility location problem is one of the most classical NP-hard problems in combinatorial optimization. In the metric facility location problem (MFLP), we are given a set of facilities, a set of clients and the metric distances between facilities and clients. In this paper, we consider the squared metric facility location problem (SMFLP) with nonuniform capacities, where each facility has a nonuniform capacity to serve a limited amount of client demands, and the distances between facilities and clients are no longer metric but squared metric. Fernandes et al. (2015) analyze the LP-based algorithms for the MFLP when they are applied to the SMFLP and achieve constant approximation ratios. In this paper, we do the same thing on local search algorithm, one of the most powerful techniques for MFLP with nonuniform capacities. Particularly, we propose the first constant approximation algorithm with approximation ratio 13+ϵ for the SMFLP with nonuniform capacities.