Power domination with random sensor failure
Combinatorics
2023-12-20 v1
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 , we study the expected number of observed vertices at the termination of the fragile power domination process. This expected value is a polynomial in , 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.
Keywords
Cite
@article{arxiv.2312.12259,
title = {Power domination with random sensor failure},
author = {Beth Bjorkman and Zachary Brennan and Mary Flagg and Johnathan Koch},
journal= {arXiv preprint arXiv:2312.12259},
year = {2023}
}
Comments
20 pages, 6 figures