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

Content Provider	Springer Nature Link
Author	Pedrosa, Lehilton L. C. Miyazawa, Flávio K. Fernandes, Cristina G. Meira, Luis A. A.
Copyright Year	2014
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 $$\mathrm{P} \ne \mathrm{NP} $$ . 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 dual-fitting analysis of the primal-dual algorithms for both the SMFLP and the MFLP, improving some of the previous analysis for the MFLP.
Ending Page	685
Page Count	31
Starting Page	655
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	2
Volume Number	153
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-09-30
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical Methods in Physics Calculus of Variations and Optimal Control; Optimization Mathematics of Computing Numerical Analysis Theoretical, Mathematical and Computational Physics Approximation algorithms Linear programming Combinatorial optimization Discrete location and assignment Combinatorics
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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