Parameterized Complexity of Minimum Membership Dominating Set

NONBLOCKER: Parameterized Algorithmics for minimum dominating set

We provide parameterized algorithms for nonblocker, the parametric dual of the well known dominating set problem. We exemplify three methodologies for deriving parameterized algorithms that can be used in other circumstances as well, including the (i) use of extremal combinatorics (known results from graph theory) in order to obtain very small kernels, (ii) use of known exact algorithms for the...

On the Parameterized Complexity of Approximating Dominating Set

We study the parameterized complexity of approximating the k-Dominating Set (DomSet) problem where an integer k and a graph G on n vertices are given as input, and the goal is to find a dominating set of size at most F(k) · k whenever the graph G has a dominating set of size k. When such an algorithm runs in time T(k) · poly(n) (i.e., FPT-time) for some computable function T, it is said to be a...

Parameterized Planar Dominating Set

Parameterized Planar Dominating Set 21

A note on the complexity of minimum dominating set

The currently (asymptotically) fastest algorithm for minimum dominating set on graphs of n nodes is the trivial (2n) algorithm which enumerates and checks all the subsets of nodes. In this paper we present a simple algorithm which solves this problem in O(1.81n) time.  2005 Published by Elsevier B.V.