An exact algorithm for the maximum probabilistic clique problem
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- Miao, Z., Balasundaram, B. & Pasiliao, E.L. J Comb Optim (2014) 28: 105. doi:10.1007/s10878-013-9699-4
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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.