A Simple Algorithm for Solving the Power Domination Problem on Grid Graphs

The power domination problem is a variant of the classical domination problem in graphs and is defined as follows. Given an undirected graph G = (V,E), the problem is to find a minimum vertex set P ⊆ V , called the power dominating set of G, such that all vertices in G are observed by the vertices of P . Herein, a vertex observes itself and all its neighbors, and if an observed vertex has all but one of its neighbors observed, then the remaining neighbor becomes observed as well. The minimum cardinality of a power dominating set of a graph is its power domination number. In [1], Dorfling and Henning determined the power domination number of an n × m grid graph. Their proof provides an algorithm for solving such a problem on grid graphs. In this paper, we present a simpler algorithm for solving the same problem.