Beyond O*(2^n) in domination-type problems

In this paper we provide algorithms faster thanO(2) for several NP-complete dominationtype problems. More precisely, we provide: • an algorithm for CAPACITATED DOMINATING SET that solves it in O(1.89), • a branch-and-reducealgorithm solving LARGEST IRREDUNDANT SET inO(1.9657) time, • and a simple iterative-DFS algorithm for SMALLEST INCLUSION-MAXIMAL IRREDUNDANT SET that solves it in O(1.999956n) time. We also provide an exponential approximation scheme for CAPACITATED DOMINATING SET. All algorithms require polynomial space. Despite the fact that the discussed problems are quite similar to the DOMINATING SET problem, we are not aware of any published algorithms solving these problems faster than the obvious O(2) solution prior to this paper.