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# CO seminar – Mary Flagg

## May 24 @ 12:30 - 13:30

**Location:** MF 3

**Speaker: **Mary Flagg (University of St. Thomas – Houston)

**Title: **Redundance for Power Domination and Zero Forcing

**Abstract: **

Power domination is the graph theory model of the PMU Placement Problem in electrical engineering. A phasor measurement unit (PMU) is a sensor used to monitor the electric grid in real time, and the optimization problem is to determine the minimum number of PMUs necessary to monitor the grid, and where to place them. Power domination is closely related to zero forcing, a propagation game on a simple graph that has been developed independently in the linear algebra community, control of quantum systems and graph searching. The optimal solutions to the power domination or zero forcing process yields a minimum solution. However, it is often desirable to add some redundancy to the solution so that the chosen solution observed the graph even when something breaks. Finding redundant solutions also relates to the idea of reconfiguration, transforming one solution into another. I will share my work on examining power domination and zero forcing with faulty vertices or edges, and reconfiguring one power dominating or zero forcing set into another.