Power Domination in $\mathcal{O}^*(1.7548^n)$ Using Reference Search Trees

Abstract

The Power Dominating Set problem is an extension of the well-known domination problem on graphs in a way that we enrich it by a second propagation rule: Given a graph G(V,E) a set P ⊆ V is a power dominating set if every vertex is observed after we have applied the next two rules exhaustively. First, a vertex is observed if v e P or it has a neighbor in P. Secondly, if an observed vertex has exactly one unobserved neighbor u, then also u will be observed as well. We show that Power Dominating Set remains $\mathcal{NP}$-hard on cubic graphs. We designed an algorithm solving this problem in time $\mathcal{O}^*(1.7548^n)$ on general graphs. To achieve this we have used a new notion of search trees called reference search trees providing non-local pointers.