Clustering through Continuous Facility Location Problems

Autor(es)

Meira, Luis A. A. ; Miyazawa, Flavio K. ; Pedrosa, Lehilton L. C.

• Tipo de documento: Artigo Científico
• Fonte: THEORETICAL COMPUTER SCIENCE; v. 657, p. 9-pg., 2017-01-02.

Resumo

We consider the Continuous Facility Location Problem (ConFLP). Given a finite set of clients C subset of R-d and a number f is an element of R+, ConFLP consists in opening a set F' subset of R-d of facilities, each at cost f, and connecting each client to an open facility. The objective is to minimize the costs of opening facilities and connecting clients. We reduce ConFLP to the standard Facility Location Problem (FLP), by using the so-called approximate center sets. This reduction preserves the approximation, except for an error epsilon, and implies 1.488 + epsilon and 2.04 + epsilon-approximations when the connection cost is given by the Euclidean distance and the squared Euclidean distance, respectively. Moreover, we obtain approximate center sets for the case that the connection cost is the ath power of the Euclidean distance, achieving approximations for the corresponding problems, for any alpha >= 1. As a byproduct, we also obtain a polynomial-time approximation scheme for the k-median problem with this cost function, for any fixed k. (C) 2016 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 10/20710-4 - Algoritmos de Aproximação para Problemas de Localização com Diferentes Funções de Distância
• Beneficiário: Lehilton Lelis Chaves Pedrosa
• Modalidade de apoio: Bolsas no Brasil - Doutorado