Universal Facility Location in Generalized Metric Space

Abstract

We consider the universal facility location that extends several classical facility location problems like the incremental-cost facility location, concave-cost facility location, hard-capacitated facility location, soft-capacitated facility location, and of course, uncapacitated facility location. In this problem we are given a set of facilities ${\mathcal {F}}$ and clients ${\mathcal {C}}$, as well as the distances between any pair of facility and client. Each facility i has its specific cost function $f_i(\cdot )$ depending on the amount of clients assigned to that facility. The goal is to assign the clients to facilities such that the sum of facility and service costs is minimized. In metric facility location, the service cost is proportional to the distance between the client and its assigned facility. We study a cost measure known as $l_2^2$ considered by Jain and Vazirani [J. ACM’01] and Fernandes et al. [Math. Program.’15] where the service cost is proportional to the squared distance. We extend their work to include the aforementioned variants of facility location. As our main contribution, a local search based $(11.18+\varepsilon )$-approximation algorithm is proposed.