Minimum cost b-matching problems with neighborhoods

In this paper, we deal with minimum cost b -matching problems on graphs where the nodes are assumed to belong to non-necessarily convex regions called neighborhoods, and the costs are given by the distances between points of the neighborhoods. The goal in the proposed problems is twofold: (i) findin...

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Bibliographic Details
Published in:Computational optimization and applications 2022-11, Vol.83 (2), p.525-553
Main Authors: Espejo, I., Páez, R., Puerto, J., Rodríguez-Chía, A. M.
Format: Article
Language:English
Subjects:
Algorithms
Convex and Discrete Geometry
Costs
Graphs
Linear programming
Management Science
Matching
Mathematics
Mathematics and Statistics
Minimum cost
Mixed integer
Neighborhoods
Nonlinear programming
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
Telecommunications towers
Traveling salesman problem
Wireless networks
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Summary:In this paper, we deal with minimum cost b -matching problems on graphs where the nodes are assumed to belong to non-necessarily convex regions called neighborhoods, and the costs are given by the distances between points of the neighborhoods. The goal in the proposed problems is twofold: (i) finding a b -matching in the graph and (ii) determining a point in each neighborhood to be the connection point among the edges defining the b-matching. Different variants of the minimum cost b -matching problem are considered depending on the criteria to match neighborhoods: perfect, maximum cardinality, maximal and the a – b -matching problems. The theoretical complexity of solving each one of these problems is analyzed. Different mixed integer non-linear programming formulations are proposed for each one of the considered problems and then reformulated as Second Order Cone formulations. An extensive computational experience shows the efficiency of the proposed formulations to solve the problems under study.
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-022-00406-7