Failure filtrations for fenced sensor networks

Journal Article (Journal Article)

In this paper we consider the question of sensor network coverage for a two-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 it is part of a slightly larger class of problems which is #P-hard, and thus fast algorithms likely do not exist unless P = NP. The question of whether the specific problem is, in fact, #P-hard remains open. 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 to give an early warning of potential failure. These algorithms build on the theory of topological persistence. © The Author(s) 2012.

Full Text

Duke Authors

Cited Authors

  • Munch, E; Shapiro, M; Harer, J

Published Date

  • August 1, 2012

Published In

Volume / Issue

  • 31 / 9

Start / End Page

  • 1044 - 1056

Electronic International Standard Serial Number (EISSN)

  • 1741-3176

International Standard Serial Number (ISSN)

  • 0278-3649

Digital Object Identifier (DOI)

  • 10.1177/0278364912451671

Citation Source

  • Scopus