Approximation algorithms for the single allocation problem in hub-and-spoke networks and related metric labeling problems

This paper deals with a single allocation problem in hub-and-spoke networks. We present a simple deterministic 3-approximation algorithm and randomized 2-approximation algorithm based on a linear relaxation problem and a randomized rounding procedure. We handle the case where the number of hubs is t...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 157; no. 9; pp. 2078 - 2088
Main Authors: Iwasa, Masaru, Saito, Hiroo, Matsui, Tomomi
Format: Journal Article Conference Proceeding
Language:English
Published: Kidlington Elsevier B.V 06.05.2009
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Approximation algorithm
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Dependent rounding
Exact sciences and technology
General topology
Hub location
Mathematics
Metric labeling
Sciences and techniques of general use
Theoretical computing
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Metric labeling
Dependent rounding
Approximation algorithm
Hub location
Approximation
Metric space
Computer theory
Label
Optimization
Relaxation
Network
Procedure
Object
Combinatorics
Deterministic algorithms
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:This paper deals with a single allocation problem in hub-and-spoke networks. We present a simple deterministic 3-approximation algorithm and randomized 2-approximation algorithm based on a linear relaxation problem and a randomized rounding procedure. We handle the case where the number of hubs is three, which is known to be NP-hard, and present a (5/4)-approximation algorithm. The single allocation problem includes a special class of the metric labeling problem, defined by introducing an assumption that both objects and labels are embedded in a common metric space. Under this assumption, we can apply our algorithms to the metric labeling problem without losing theoretical approximation ratios. As a byproduct, we also obtain a (4/3)-approximation algorithm for an ordinary metric labeling problem with three labels.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2008.11.016