We handle in this paper three dominating clique problems, namely, the decision problem to detect whether a graph has a dominating clique and two optimization versions asking to compute a maximum- and a minimum-size dominating clique of a graph G, if G has a dominating clique. For the three problems we propose exact moderately exponential algorithms with worst-case running time upper bounds improving those by Kratsch and Liedloff [D. Kratsch, M. Liedloff, An exact algorithm for the minimum dominating clique problem, Theoret. Comput. Sci. 385 (1-3) (2007) 226-240]. We then study the three problems in sparse and dense graphs also providing improved running time upper bounds. Finally, we propose some exponential time approximation algorithms for the optimization versions. © 2012 Elsevier B.V. All rights reserved.
Bourgeois, N., Della Croce, F., Escoffier, B., & Paschos, V. T. (2012). Algorithms for dominating clique problems. Theoretical Computer Science, 459, 77–88. https://doi.org/10.1016/j.tcs.2012.07.016