# Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem

@article{Belyi2021SubnetworkCF, title={Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem}, author={Alexander Belyi and Stanislav Sobolevsky and Alexander N. Kurbatski and Carlo Alberto Ratti}, journal={ArXiv}, year={2021}, volume={abs/2110.05627} }

We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning problem, being NP-hard in the general case of having edge weights of different signs. We propose a new method of estimating an upper bound of the objective function that we combine with the classical branch-and-bound technique to find the exact solution. We…

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