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Theoretical Computer Science - Parameterized and exact computation
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Discrete Applied Mathematics
Linear-time enumeration of isolated cliques
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AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
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Theoretical Computer Science
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Theoretical Computer Science
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In a graph G = (V,E), a vertex subset S ⊆ V of size k is called c-isolated if it has less than c ċ k outgoing edges. We repair a nontrivially flawed algorithm for enumerating all c-isolated cliques due to Ito et al. [European Symposium on Algorithms 2005] and obtain an algorithm running in O(4c ċ c4 ċ |E|) time. We describe a speedup trick that also helps parallelizing the enumeration. Moreover, we introduce a more restricted and a more general isolation concept and show that both lead to faster enumeration algorithms. Finally, we extend our considerations to s-plexes (a relaxation of the clique notion), pointing out a W[1]-hardness result and providing a fixed-parameter algorithm for enumerating isolated s-plexes.