Subnetwork constraints for tighter upper bounds and exact solution of the clique partitioning problem
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186_2023_Article_835.pdf
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824c1ef0340bc9b5fa7ea59b577625a6
Author(s)
Belyi, Alexander
Sobolevsky, Stanislav
Kurbatski, Alexander
Ratti, Carlo
Date Issued
September 9, 2023
Publisher
Springer Berlin Heidelberg
Citation
Belyi, Alexander, Sobolevsky, Stanislav, Kurbatski, Alexander and Ratti, Carlo. 2023. "Subnetwork constraints for tighter upper bounds and exact solution of the clique partitioning problem."
Version
Final published version
Abstract
Abstract
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.
MIT Department
Senseable City Laboratory
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s00186-023-00835-y
