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
Solving connected dominating set faster than 2n
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Exponential time algorithms for the minimum dominating set problem on some graph classes
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Exact computation of maximum induced forest
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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
Parameterized Complexity
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Threshold dominating cliques in random graphs and interval routing
Journal of Discrete Algorithms
Exact Algorithms for Dominating Clique Problems
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Random instances of W[2]-complete problems: thresholds, complexity, and algorithms
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Exact algorithms for dominating set
Discrete Applied Mathematics
Polynomial space algorithms for counting dominating sets and the domatic number
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
A detailed study of the dominating cliques phase transition in random graphs
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Algorithms for dominating clique problems
Theoretical Computer Science
Information Processing Letters
| Hi-index | 5.23 |
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 problems are NP-hard. We present an O(1.3387n) 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 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 the algorithm. Finally using memorization we obtain an O(1.3234n) time and exponential space algorithm for the same problem.