An Exact Algorithm for the Minimum Dominating Clique Problem

@article{Kratsch2006AnEA,
  title={An Exact Algorithm for the Minimum Dominating Clique Problem},
  author={Dieter Kratsch and Mathieu Liedloff},
  journal={Theor. Comput. Sci.},
  year={2006},
  volume={385},
  pages={226-240}
}
A subset of vertices D ⊆ V of a graph G = (V, E) is a dominating clique if D is a dominating set and a clique of G. The existence problem ‘Given a graph G, is there a dominating clique in G?’ is NP-complete, and thus both the Minimum and the Maximum Dominating Clique problem are NP-hard. We present an O(1.3387) time and polynomial space algorithm that for an input graph on n vertices either computes a minimum dominating clique or reports that the graph has no dominating clique. The algorithm… CONTINUE READING