Failure Filtrations for Fenced Sensor Networks

TL;DR

This paper investigates sensor network coverage probability using topological persistence, providing complexity results and algorithms for small and large sensor sets based on failure data.

Contribution

It extends coverage analysis to probabilistic, non-metric sensor networks and introduces algorithms leveraging topological persistence for failure detection.

Findings

Coverage problem is #P-complete.

Deterministic algorithm feasible for small sensor sets.

Dynamic algorithm based on new topological coverage criterion.

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.