An Exact 2.9416^n Algorithm for the Three Domatic Number Problem

Details An Exact 2.9416^n Algorithm for the Three Domatic Number Problem An Exact 2.9416^n Algorithm for the Three Domatic Number Problem

2005-06-24

arxiv.org/abs/cs/0506090v1

Computer Science

Computational Complexity

20 pages, 1 figure

Scientific paper

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 3^n, up to polynomial factors. In this paper, we design an exact deterministic algorithm for this problem running in time 2.9416^n. 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.

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