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An exact algorithm for the maximum probabilistic clique problem

Author

Listed:
  • Zhuqi Miao

    (Oklahoma State University)

  • Balabhaskar Balasundaram

    (Oklahoma State University)

  • Eduardo L. Pasiliao

    (Munitions Directorate, Air Force Research Laboratory)

Abstract

The maximum clique problem is a classical problem in combinatorial optimization that has a broad range of applications in graph-based data mining, social and biological network analysis and a variety of other fields. This article investigates the problem when the edges fail independently with known probabilities. This leads to the maximum probabilistic clique problem, which is to find a subset of vertices of maximum cardinality that forms a clique with probability at least $$\theta \in [0,1]$$ θ ∈ [ 0 , 1 ] , which is a user-specified probability threshold. We show that the probabilistic clique property is hereditary and extend a well-known exact combinatorial algorithm for the maximum clique problem to a sampling-free exact algorithm for the maximum probabilistic clique problem. The performance of the algorithm is benchmarked on a test-bed of DIMACS clique instances and on a randomly generated test-bed.

Suggested Citation

  • Zhuqi Miao & Balabhaskar Balasundaram & Eduardo L. Pasiliao, 2014. "An exact algorithm for the maximum probabilistic clique problem," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 105-120, July.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:1:d:10.1007_s10878-013-9699-4
    DOI: 10.1007/s10878-013-9699-4
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    References listed on IDEAS

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    1. Svyatoslav Trukhanov & Chitra Balasubramaniam & Balabhaskar Balasundaram & Sergiy Butenko, 2013. "Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations," Computational Optimization and Applications, Springer, vol. 56(1), pages 113-130, September.
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    Cited by:

    1. Oleksandra Yezerska & Sergiy Butenko & Vladimir L. Boginski, 2018. "Detecting robust cliques in graphs subject to uncertain edge failures," Annals of Operations Research, Springer, vol. 262(1), pages 109-132, March.

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