Journal of Combinatorial Optimization

, Volume 28, Issue 1, pp 105–120 | Cite as

An exact algorithm for the maximum probabilistic clique problem

  • Zhuqi Miao
  • Balabhaskar Balasundaram
  • Eduardo L. Pasiliao


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 \(\theta \in [0,1]\), 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.


Maximum clique problem Probabilistic programming  Probabilistic clique Branch-and-bound 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Zhuqi Miao
    • 1
  • Balabhaskar Balasundaram
    • 1
  • Eduardo L. Pasiliao
    • 2
  1. 1.School of Industrial Engineering & ManagementOklahoma State UniversityStillwater USA
  2. 2.Munitions Directorate, Air Force Research LaboratoryEglin AFBUSA

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