{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/subnetwork-constraints-for-tighter-upper","title":"Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem","arxiv_id":"2110.05627","date":"2021-10-11","proceeding":null,"authors":["Alexander Belyi","Stanislav Sobolevsky","Alexander Kurbatski","Carlo Ratti"],"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.","url_abs":"https://arxiv.org/abs/2110.05627v2","url_pdf":"https://arxiv.org/pdf/2110.05627v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"subnetwork-constraints-for-tighter-upper","repo_url":"https://github.com/alexander-belyi/best-partition","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}