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

Abstract

In this paper we provide algorithms faster than O*(2^n) for several NP-complete domination-type problems. More precisely, we provide: an algorithm for CAPACITATED DOMINATING SET that solves it in O(1.89^n), a branch-and-reduce algorithm solving LARGEST IRREDUNDANT SET in O(1.9657^n) time and a simple iterative-DFS algorithm for SMALLEST INCLUSION-MAXIMAL IRREDUNDANT SET that solves it in O(1.999956^n) 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^n) solution prior to this paper.