Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem
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 NPhard 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 branchandbound technique to find the exact solution. We evaluate our approach on a broad range of random graphs and realworld networks. The proposed approach provided tighter upper bounds and achieved significant convergence speed improvements compared to known alternative methods.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.05627
 Bibcode:
 2021arXiv211005627B
 Keywords:

 Computer Science  Social and Information Networks;
 Computer Science  Discrete Mathematics;
 Mathematics  Optimization and Control;
 Physics  Data Analysis;
 Statistics and Probability;
 05C85;
 68T09;
 68R10;
 90C35;
 90C90;
 91C20;
 G.2.2;
 I.5.3;
 I.2.8
 EPrint:
 20 pages, 3 figures