A constant factor approximation algorithm for the fault-tolerant facility location problem

We consider a generalization of the classical facility location problem, where we require the solution to be fault-tolerant. In this generalization, every demand point j must be served by r j facilities instead of just one. The facilities other than the closest one are “backup” facilities for that d...

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Bibliographic Details
Published in:Journal of algorithms Vol. 48; no. 2; pp. 429 - 440
Main Authors: Guha, Sudipto, Meyerson, Adam, Munagala, Kamesh
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.09.2003
Elsevier
Subjects:
Applied sciences
Approximation algorithm
Exact sciences and technology
Facility location
Fault tolerance
Flows in networks. Combinatorial problems
Operational research and scientific management
Operational research. Management science
Facility location
Approximation algorithm
Fault tolerance
Costs
Filtering
Program
Constant
Use
Routing
Generalization
Location problem
Weight
Numerical approximation
Assignment
Integer
Relaxation
Randomization
Type
Linear combination
Technique
Application
Link
Fault tolerant system
ISSN:0196-6774, 1090-2678
Online Access:Get full text
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Summary:We consider a generalization of the classical facility location problem, where we require the solution to be fault-tolerant. In this generalization, every demand point j must be served by r j facilities instead of just one. The facilities other than the closest one are “backup” facilities for that demand, and any such facility will be used only if all closer facilities (or the links to them) fail. Hence, for any demand point, we can assign nonincreasing weights to the routing costs to farther facilities. The cost of assignment for demand j is the weighted linear combination of the assignment costs to its r j closest open facilities. We wish to minimize the sum of the cost of opening the facilities and the assignment cost of each demand  j. We obtain a factor 4 approximation to this problem through the application of various rounding techniques to the linear relaxation of an integer program formulation. We further improve the approximation ratio to 3.16 using randomization and to 2.41 using greedy local-search type techniques.
ISSN:0196-6774
1090-2678
DOI:10.1016/S0196-6774(03)00056-7