On generating all maximal independent sets
Information Processing Letters
Discrete Mathematics - Topics on domination
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Exact computation of maximum induced forest
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Measure and conquer: domination – a case study
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Algorithmics in exponential time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Exact (exponential) algorithms for the dominating set problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Improved exponential-time algorithms for treewidth and minimum fill-in
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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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(1.3390n) time 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 uses the Branch & Reduce paradigm and its time analysis is based on the Measure & Conquer approach. We also establish a lower bound of Ω(1.2599n) for the worst case running time of our algorithm.