An exact approach for the multi-constraint graph partitioning problem

In this work, a multi-constraint graph partitioning problem is introduced. The input is an undirected graph with costs on the edges and multiple weights on the nodes. The problem calls for a partition of the node set into a fixed number of clusters, such that each cluster satisfies a collection of n...

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Bibliographic Details
Published inEURO journal on computational optimization Vol. 8; no. 3-4; pp. 289 - 308
Main Authors Recalde, Diego, Torres, Ramiro, Vaca, Polo
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Elsevier Ltd 01.10.2020
Springer Berlin Heidelberg
Springer Nature B.V
Elsevier
Subjects
05C70
90C10
90C27
90C57
Algorithms
Branch & Cut
Business and Management
Clusters
Graph partitioning
Graph theory
Integer programming
Management Science
Nodes
Operations Management
Operations Research
Operations Research/Decision Theory
Optimization
Original Paper
Partitioning
Graph partitioning
Integer programming
90C10
Branch & Cut
90C57
05C70
90C27
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Summary:In this work, a multi-constraint graph partitioning problem is introduced. The input is an undirected graph with costs on the edges and multiple weights on the nodes. The problem calls for a partition of the node set into a fixed number of clusters, such that each cluster satisfies a collection of node weight constraints, and the total cost of the edges whose end nodes are in the same cluster is minimized. It arises as a sub-problem of an integrated vehicle and pollster problem from a real-world application. Two integer programming formulations are provided, and several families of valid inequalities associated with the respective polyhedra are proved. An exact algorithm based on Branch & Bound and cutting planes is proposed, and it is tested on real-world instances.
ISSN:2192-4406
2192-4414
DOI:10.1007/s13675-020-00126-9