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On robust clusters of minimum cardinality in networks

Author

Listed:
  • Chitra Balasubramaniam

    (Texas A&M University)

  • Sergiy Butenko

    (Texas A&M University)

Abstract

This paper studies two clique relaxation models, k-blocks and k-robust 2-clubs, used to describe structurally cohesive clusters with good robustness and reachability properties. The minimization version of the two problems are shown to be hard to approximate for $$k \ge 3$$ k ≥ 3 and $$k \ge 4$$ k ≥ 4 , respectively. Integer programming formulations are proposed and a polyhedral study is presented. The results of sample numerical experiments on several graph instances are also reported.

Suggested Citation

  • Chitra Balasubramaniam & Sergiy Butenko, 2017. "On robust clusters of minimum cardinality in networks," Annals of Operations Research, Springer, vol. 249(1), pages 17-37, February.
    • Handle: RePEc:spr:annopr:v:249:y:2017:i:1:d:10.1007_s10479-015-1992-4
    DOI: 10.1007/s10479-015-1992-4
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    References listed on IDEAS

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    1. Anurag Verma & Austin Buchanan & Sergiy Butenko, 2015. "Solving the Maximum Clique and Vertex Coloring Problems on Very Large Sparse Networks," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 164-177, February.
    2. Changcun Ma & Donghyun Kim & Yuexuan Wang & Wei Wang & Nassim Sohaee & Weili Wu, 2010. "Hardness of k-Vertex-Connected Subgraph Augmentation Problem," Journal of Combinatorial Optimization, Springer, vol. 20(3), pages 249-258, October.
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    4. Veremyev, Alexander & Boginski, Vladimir, 2012. "Identifying large robust network clusters via new compact formulations of maximum k-club problems," European Journal of Operational Research, Elsevier, vol. 218(2), pages 316-326.
    5. Balabhaskar Balasundaram & Sergiy Butenko & Svyatoslav Trukhanov, 2005. "Novel Approaches for Analyzing Biological Networks," Journal of Combinatorial Optimization, Springer, vol. 10(1), pages 23-39, August.
    6. 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.
    7. James Moody & Douglas R. White, 2000. "Structural Cohesion and Embeddedness: A Hierarchical Conception of Social Groups," Working Papers 00-08-049, Santa Fe Institute.
    8. R. Luce & Albert Perry, 1949. "A method of matrix analysis of group structure," Psychometrika, Springer;The Psychometric Society, vol. 14(2), pages 95-116, June.
    9. Pattillo, Jeffrey & Youssef, Nataly & Butenko, Sergiy, 2013. "On clique relaxation models in network analysis," European Journal of Operational Research, Elsevier, vol. 226(1), pages 9-18.
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    Cited by:

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