An exact algorithm for the maximum probabilistic clique problem

Zhuqi Miao (), Balabhaskar Balasundaram () and Eduardo L. Pasiliao ()
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Zhuqi Miao: Oklahoma State University
Balabhaskar Balasundaram: Oklahoma State University
Eduardo L. Pasiliao: Munitions Directorate, Air Force Research Laboratory

Journal of Combinatorial Optimization, 2014, vol. 28, issue 1, No 7, 105-120

Abstract: 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.

Keywords: Maximum clique problem; Probabilistic programming; Probabilistic clique; Branch-and-bound (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-013-9699-4

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