English

Failure Filtrations for Fenced Sensor Networks

Computational Geometry 2016-04-12 v1

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 P==NP. 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.

Keywords

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}
}
R2 v1 2026-06-21T19:12:35.926Z