An Improved Exact Algorithm for the Domatic Number Problem [article]

Tobias Riege, Jörg Rothe, Holger Spakowski, Masaki Yamamoto
2006 arXiv   pre-print
The 3-domatic number problem asks whether a given graph can be partitioned intothree dominating sets. We prove that this problem can be solved by a deterministic algorithm in time 2.695^n (up to polynomial factors). This result improves the previous bound of 2.8805^n, which is due to Fomin, Grandoni, Pyatkin, and Stepanov. To prove our result, we combine an algorithm by Fomin et al. with Yamamoto's algorithm for the satisfiability problem. In addition, we show that the 3-domatic number problem
more » ... an be solved for graphs G with bounded maximum degree Delta(G) by a randomized algorithm, whose running time is better than the previous bound due to Riege and Rothe whenever Delta(G) >= 5. Our new randomized algorithm employs Schoening's approach to constraint satisfaction problems.
arXiv:cs/0603060v1 fatcat:tthcokzv7fe53h4gwwasry3jky