A systematic approach to bound factor-revealing LPs and its application to the metric and squared metric facility location problems

Author(s)

Fernandes, Cristina G. ^[1] ; Meira, Luis A. A. ^[2] ; Miyazawa, Flavio K. ^[3] ; Pedrosa, Lehilton L. C. ^[3]

Affiliation

^[1] Univ Sao Paulo, Dept Comp Sci, Sao Paulo - Brazil

^[2] Univ Estadual Campinas, Sch Technol, Campinas, SP - Brazil

^[3] Univ Estadual Campinas, Inst Comp, Campinas, SP - Brazil

• Document type: Journal article
• Source: MATHEMATICAL PROGRAMMING; v. 153, n. 2, p. 655-685, NOV 2015.
• Web of Science Citations: 6

Abstract

A systematic technique to bound factor-revealing linear programs is presented. We show how to derive a family of upper bound factor-revealing programs (UPFRP), and show that each such program can be solved by a computer to bound the approximation factor of an associated algorithm. Obtaining an UPFRP is straightforward, and can be used as an alternative to analytical proofs, that are usually very long and tedious. We apply this technique to the metric facility location problem (MFLP) and to a generalization where the distance function is a squared metric. We call this generalization the squared metric facility location problem (SMFLP), and prove that there is no approximation factor better than 2.04, assuming P not equal NP. Then, we analyze the best known algorithms for the MFLP based on primal-dual and LP-rounding techniques when they are applied to the SMFLP. We prove very tight bounds for these algorithms, and show that the LP-rounding algorithm achieves a ratio of 2.04, and therefore has the best possible factor for the SMFLP. We use UPFRPs in the dualfitting analysis of the primal-dual algorithms for both the SMFLP and the MFLP, improving some of the previous analysis for the MFLP. (AU)

• FAPESP's process: 10/20710-4 - Approximation Algorithms for Facility Location Problems with Different Distance Functions
• Grantee: Lehilton Lelis Chaves Pedrosa
• Support Opportunities: Scholarships in Brazil - Doctorate