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A branch-and-bound approach for maximum quasi-cliques

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  • Foad Mahdavi Pajouh
  • Zhuqi Miao
  • Balabhaskar Balasundaram

Abstract

Detecting quasi-cliques in graphs is a useful tool for detecting dense clusters in graph-based data mining. Particularly in large-scale data sets that are error-prone, cliques are overly restrictive and impractical. Quasi-clique detection has been accomplished using heuristic approaches in various applications of graph-based data mining in protein interaction networks, gene co-expression networks, and telecommunication networks. Quasi-cliques are not hereditary, in the sense that every subset of a quasi-clique need not be a quasi-clique. This lack of heredity introduces interesting challenges in the development of exact algorithms to detect maximum cardinality quasi-cliques. The only exact approaches for this problem are limited to two mixed integer programming formulations that were recently proposed in the literature. The main contribution of this article is a new combinatorial branch-and-bound algorithm for the maximum quasi-clique problem. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Foad Mahdavi Pajouh & Zhuqi Miao & Balabhaskar Balasundaram, 2014. "A branch-and-bound approach for maximum quasi-cliques," Annals of Operations Research, Springer, vol. 216(1), pages 145-161, May.
    • Handle: RePEc:spr:annopr:v:216:y:2014:i:1:p:145-161:10.1007/s10479-012-1242-y
    DOI: 10.1007/s10479-012-1242-y
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    References listed on IDEAS

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    2. Balabhaskar Balasundaram & Sergiy Butenko & Illya V. Hicks, 2011. "Clique Relaxations in Social Network Analysis: The Maximum k -Plex Problem," Operations Research, INFORMS, vol. 59(1), pages 133-142, February.
    3. Robert Mokken, 1979. "Cliques, clubs and clans," Quality & Quantity: International Journal of Methodology, Springer, vol. 13(2), pages 161-173, April.
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    Cited by:

    1. Alexander Veremyev & Oleg A. Prokopyev & Sergiy Butenko & Eduardo L. Pasiliao, 2016. "Exact MIP-based approaches for finding maximum quasi-cliques and dense subgraphs," Computational Optimization and Applications, Springer, vol. 64(1), pages 177-214, May.
    2. Wu, Qinghua & Hao, Jin-Kao, 2015. "A review on algorithms for maximum clique problems," European Journal of Operational Research, Elsevier, vol. 242(3), pages 693-709.
    3. Zhou, Yi & Lin, Weibo & Hao, Jin-Kao & Xiao, Mingyu & Jin, Yan, 2022. "An effective branch-and-bound algorithm for the maximum s-bundle problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 27-39.
    4. Zhou, Qing & Benlic, Una & Wu, Qinghua, 2020. "An opposition-based memetic algorithm for the maximum quasi-clique problem," European Journal of Operational Research, Elsevier, vol. 286(1), pages 63-83.
    5. Zhuqi Miao & Balabhaskar Balasundaram, 2020. "An Ellipsoidal Bounding Scheme for the Quasi-Clique Number of a Graph," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 763-778, July.
    6. Rysz, Maciej & Mahdavi Pajouh, Foad & Pasiliao, Eduardo L., 2018. "Finding clique clusters with the highest betweenness centrality," European Journal of Operational Research, Elsevier, vol. 271(1), pages 155-164.
    7. Veremyev, Alexander & Prokopyev, Oleg A. & Boginski, Vladimir & Pasiliao, Eduardo L., 2014. "Finding maximum subgraphs with relatively large vertex connectivity," European Journal of Operational Research, Elsevier, vol. 239(2), pages 349-362.

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