Combinatorial bounds via measure and conquer

Fedor V. Fomin, Fabrizio Grandoni, Artem V. Pyatkin, Alexey A. Stepanov
2008 ACM Transactions on Algorithms  
We provide an algorithm listing all minimal dominating sets of a graph on n vertices in time O(1.7159 n ). This result can be seen as an algorithmic proof of the fact that the number of minimal dominating sets in a graph on n vertices is at most 1.7159 n , thus improving on the trivial O(2 n / √ n) bound. Our result makes use of the measure and conquer technique which was recently developed in the area of exact algorithms. Based on this result, we derive an O(2.8718 n ) algorithm for the
more » ... ithm for the domatic number problem.
doi:10.1145/1435375.1435384 fatcat:yzf37wklevcvljcnuxhnju4gk4