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!
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
An improved exact algorithm for the domatic number problem
Information Processing Letters
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications
ACM Transactions on Algorithms (TALG)
Bounding the number of minimal dominating sets: a measure and conquer approach
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Polynomial space algorithms for counting dominating sets and the domatic number
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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The three domatic number problem asks whether a given undirected graph can be partitioned into at least three dominating sets, i.e., sets whose closed neighborhood equals the vertex set of the graph. Since this problem is NP-complete, no polynomial-time algorithm is known for it. The naive deterministic algorithm for this problem runs in time 3n, up to polynomial factors. In this paper, we design an exact deterministic algorithm for this problem running in time 2.9416n. Thus, our algorithm can handle problem instances of larger size than the naive algorithm in the same amount of time. We also present another deterministic and a randomized algorithm for this problem that both have an even better performance for graphs with small maximum degree.