NDLI: LP-based approximation algorithms for capacitated facility location

Content Provider	Springer Nature Link
Author	Levi, Retsef Swamy, Chaitanya Shmoys, David B.
Copyright Year	2010
Abstract	In the capacitated facility location problem with hard capacities, we are given a set of facilities, $${\mathcal{F}}$$ , and a set of clients $${\mathcal{D}}$$ in a common metric space. Each facility i has a facility opening cost f i and capacity u i that specifies the maximum number of clients that may be assigned to this facility. We want to open some facilities from the set $${\mathcal{F}}$$ and assign each client to an open facility so that at most u i clients are assigned to any open facility i. The cost of assigning client j to facility i is given by the distance c ij , and our goal is to minimize the sum of the facility opening costs and the client assignment costs. The only known approximation algorithms that deliver solutions within a constant factor of optimal for this NP-hard problem are based on local search techniques. It is an open problem to devise an approximation algorithm for this problem based on a linear programming lower bound (or indeed, to prove a constant integrality gap for any LP relaxation). We make progress on this question by giving a 5-approximation algorithm for the special case in which all of the facility costs are equal, by rounding the optimal solution to the standard LP relaxation. One notable aspect of our algorithm is that it relies on partitioning the input into a collection of single-demand capacitated facility location problems, approximately solving them, and then combining these solutions in a natural way.
Ending Page	379
Page Count	15
Starting Page	365
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1-2
Volume Number	131
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-05-18
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical Methods in Physics Mathematics of Computing Calculus of Variations and Optimal Control; Optimization Transportation, logistics Numerical Analysis Theoretical, Mathematical and Computational Physics Combinatorics
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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