On the Power Domination Problem in Graphs
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A crucial task for electric power companies consists of the continuous monitoring of their power network. This monitoring can be efficiently accomplished by placing phase measurement units (PMUs) at selected network locations. However, due to the high cost of the PMUs, their number must be minimized . Finding the minimum number of PMUs needed to monitor a given power network, as well as to determine the locations where the PMUs should be placed, give rise to the power domination problem in graph theory .
The power dominating problem is NP-complete, that is, there is no efficient way of finding a minimal power dominating set for a graph. However, closed formulas for the power domination number of certain families of graphs, such as rectangular grids  have been found.