An exact approach for the multi-constraint graph partitioning problem

Abstract

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.

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Acknowledgements

This research was funded by Escuela Politécnica Nacional (project PII-DM-01-2018). Moreover, we are grateful to the anonymous referees for their useful comments which led to a significantly improved presentation of this work.

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Correspondence to Ramiro Torres.

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Recalde, D., Torres, R. & Vaca, P. An exact approach for the multi-constraint graph partitioning problem. EURO J Comput Optim (2020). https://doi.org/10.1007/s13675-020-00126-9

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Keywords

  • Graph partitioning
  • Integer programming
  • Branch & Cut

Mathematics Subject Classification

  • 90C10
  • 90C27
  • 90C57
  • 05C70