An Exact Exponential Time Algorithm for Power Dominating Set
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 subset of V is a power dominating set if every vertex is observed after the exhaustive application of the following two rules. First, a vertex is observed if v. 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 NP-hard on cubic graphs. We design an algorithm solving this problem in time O*(1.7548(n)) on general graphs, using polynomial space only. To achieve this, we introduce so-called reference search trees that can be seen as a compact representation of usual search trees, providing non-local pointers in order to indicate pruned subtrees.
domination-type problems moderately exponential time algorithms np-hardness results measure and conquer