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Lagrangian relaxation and pegging test for the clique partitioning problem

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  • Noriyoshi Sukegawa
  • Yoshitsugu Yamamoto
  • Liyuan Zhang

Abstract

The clique partitioning problem is an NP-hard combinatorial optimization problem with applications to data analysis such as clustering. Though a binary integer linear programming formulation has been known for years, one needs to deal with a huge number of variables and constraints when solving a large instance. In this paper, we propose a size reduction algorithm which is based on the Lagrangian relaxation and the pegging test, and verify its validity through numerical experiments. We modify the conventional subgradient method in order to manage the high dimensionality of the Lagrangian multipliers, and also make an improvement on the ordinary pegging test by taking advantage of the structural property of the clique partitioning problem. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Noriyoshi Sukegawa & Yoshitsugu Yamamoto & Liyuan Zhang, 2013. "Lagrangian relaxation and pegging test for the clique partitioning problem," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(4), pages 363-391, December.
    • Handle: RePEc:spr:advdac:v:7:y:2013:i:4:p:363-391
    DOI: 10.1007/s11634-013-0135-5
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    References listed on IDEAS

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    Cited by:

    1. Ramazan Ünlü & Petros Xanthopoulos, 2019. "A weighted framework for unsupervised ensemble learning based on internal quality measures," Annals of Operations Research, Springer, vol. 276(1), pages 229-247, May.

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