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 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.
| Original language | English |
|---|---|
| Pages (from-to) | 105-120 |
| Number of pages | 16 |
| Journal | Journal of Combinatorial Optimization |
| Volume | 28 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jan 2014 |
| Externally published | Yes |
Keywords
- Branch-and-bound
- Maximum clique problem
- Probabilistic clique
- Probabilistic programming