Solving the maximum clique problem using a tabu search approach
Annals of Operations Research - Special issue on Tabu search
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Detection of protein complexes in protein interaction networks using n-clubs
EvoBIO'08 Proceedings of the 6th European conference on Evolutionary computation, machine learning and data mining in bioinformatics
Lower Bounds for Kernelizations and Other Preprocessing Procedures
Theory of Computing Systems
Kernel bounds for disjoint cycles and disjoint paths
Theoretical Computer Science
ADMA'06 Proceedings of the Second international conference on Advanced Data Mining and Applications
Approximating maximum diameter-bounded subgraphs
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Parameterized Complexity
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Given an undirected graph G=(V,E) and an integer ℓ≥1, the NP-hard 2-Club problem asks for a vertex set S⊆V of size at least ℓ such that the subgraph induced by S has diameter at most two. In this work, we extend previous parameterized complexity studies for 2-Club. On the positive side, we give polynomial kernels for the parameters "feedback edge set size of G" and "size of a cluster editing set of G" and present a direct combinatorial algorithm for the parameter "treewidth of G". On the negative side, we first show that unless NP⊆coNP/poly, 2-Club does not admit a polynomial kernel with respect to the "size of a vertex cover of G". Next, we show that, under the strong exponential time hypothesis, a previous O*(2|V|−ℓ) search tree algorithm [Schäfer et al., Optim. Lett. 2012] cannot be improved and that, unless NP⊆coNP/poly, there is no polynomial kernel for the dual parameter |V|−ℓ. Finally, we show that, in spite of this lower bound, the search tree algorithm for the dual parameter |V|−ℓ can be tuned into an efficient exact algorithm for 2-Club that substantially outperforms previous implementations.