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

Author

Listed:
  • Alexander Belyi

    (Masaryk University
    FM IRG, SMART Centre
    Belarusian State University)

  • Stanislav Sobolevsky

    (Masaryk University
    Masaryk University
    New York University)

  • Alexander Kurbatski

    (Belarusian State University)

  • Carlo Ratti

    (Massachusetts Institute of Technology)

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.

Suggested Citation

  • Alexander Belyi & Stanislav Sobolevsky & Alexander Kurbatski & Carlo Ratti, 2023. "Subnetwork constraints for tighter upper bounds and exact solution of the clique partitioning problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(2), pages 269-297, October.
    • Handle: RePEc:spr:mathme:v:98:y:2023:i:2:d:10.1007_s00186-023-00835-y
    DOI: 10.1007/s00186-023-00835-y
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