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Power domination with random sensor failure
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abstract
The power domination problem seeks to determine the minimum number of phasor measurement units (PMUs) needed to monitor an electric power network. We introduce random sensor failure before the power domination process occurs and call this the fragile power domination process. For a given graph, PMU placement, and probability of PMU failure $q$, we study the expected number of observed vertices at the termination of the fragile power domination process. This expected value is a polynomial in $q$, which we relate to fault-tolerant and PMU-defect-robust power domination. We also study the probability of that the entire graph becomes observed and give results for some graph families.
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On Fragile Power Domination
For fragile power domination, two graphs with equal-size sensor sets have identical expected observed-vertex polynomials exactly when their k-subset observation sums agree, and gadget constructions can freely control ...
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