Improved approximation algorithm for universal facility location problem with linear penalties

Abstract

The input of the universal facility location problem includes a set of clients and a set of facilities. Our goal is to find an assignment such that each client is assigned while the total connection and facility cost is minimized. Here the connection cost is proportional to the distance between each client and its assigned facility, thus metric. The facility cost is a nondecreasing function with respect to the total number of clients assigned to the facility. The universal facility location problem is NP-hard since it generalizes several classical facility location problems. Our work considers the universal facility location problem with linear penalties, a generalized version of the universal facility location problem. Here each client can be rejected for service with certain penalty cost. Thus we have to consider penalty cost other than total connection and facility cost in our objective function. Based on local search method, we present a (5.83+ϵ)-approximation algorithm for this problem.