Subnetwork constraints for tighter upper bounds and exact solution of the clique partitioning problem

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Authors

BELY Aliaksandr SOBOLEVSKY Stanislav ALEXANDER Kurbatski RATTI Carlo

Year of publication 2023
Type Article in Periodical
Magazine / Source Mathematical Methods of Operations Research
MU Faculty or unit

Faculty of Science

Citation
Web https://link.springer.com/article/10.1007/s00186-023-00835-y
Doi http://dx.doi.org/10.1007/s00186-023-00835-y
Keywords Clustering; Graphs; Clique partitioning problem; Community detection; Modularity; Upper bounds; Exact solution; Branch and bound; Linear programming
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Description 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 evaluate our approach on a broad range of random graphs and real-world networks. The proposed approach provided tighter upper bounds and achieved significant convergence speed improvements compared to known alternative methods.
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