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We consider a variant of the clustering problem for a complete weightedgraph. The aim is to partition the nodes into clusters maximizing the sum ofthe edge weights within the clusters. This problem is known as the cliquepartitioning problem, being NP-hard in the general case of having edge weightsof different signs. We propose a new method of estimating an upper bound of theobjective function that we combine with the classical branch-and-boundtechnique to find the exact solution. We evaluate our approach on a broad rangeof random graphs and real-world networks. The proposed approach providedtighter upper bounds and achieved significant convergence speed improvementscompared to known alternative methods.

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