Failure Filtrations for Fenced Sensor Networks
Abstract
In this paper we consider the question of sensor network coverage for a 2-dimensional domain. We seek to compute the probability that a set of sensors fails to cover given only non-metric, local (who is talking to whom) information and a probability distribution of failure of each node. This builds on the work of de Silva and Ghrist who analyzed this problem in the deterministic situation. We first show that a it is part of a slightly larger class of problems which is #P-complete, and thus fast algorithms likely do not exist unless PNP. We then give a deterministic algorithm which is feasible in the case of a small set of sensors, and give a dynamic algorithm for an arbitrary set of sensors failing over time which utilizes a new criterion for coverage based on the one proposed by de Silva and Ghrist. These algorithms build on the theory of topological persistence.
Cite
@article{arxiv.1109.6535,
title = {Failure Filtrations for Fenced Sensor Networks},
author = {Elizabeth Munch and Michael Shapiro and John Harer},
journal= {arXiv preprint arXiv:1109.6535},
year = {2016}
}