A Local Search Approximation Algorithm for a Squared Metric k-Facility Location Problem

摘要

In this paper, we introduce a squared metric fc-facility location problem (SM-fc-FLP) which is a generalization of the squared metric facility location problem (SMFLP) and fc-facility location problem (fc-FLP). In the SM-fc-FLP, we are given a client set C and a facility set T from a metric space, a facility opening cost /i > 0 for each i _ T, and an integer fc. The goal is to open a facility subset FCf with F < k and to connect each client to the nearest open facility such that the total cost (including facility opening cost and the sum of squares of distances) is minimized. Using local search and scaling techniques, we offer a constant approximation algorithm for the SM-fc-FLP.