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Parameterized Algorithmics and Computational Experiments for Finding 2-Clubs

  • Sepp Hartung
  • Christian Komusiewicz
  • André Nichterlein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7535)

Abstract

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.

Keywords

Search Tree Vertex Cover Polynomial Kernel Marked Vertex Dual Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sepp Hartung
    • 1
  • Christian Komusiewicz
    • 1
  • André Nichterlein
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany

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