Coverage Criterion in Sensor Networks Stable under Perturbation

TL;DR

This paper extends coverage criteria for sensor networks using persistent homology to account for sensor perturbations, providing a stable coverage theorem and a method to eliminate redundant coverage after perturbation.

Contribution

It introduces a stability theorem for sensor network coverage criteria under perturbation and extends the Rips interleaving theorem to a relative version.

Findings

Coverage criteria are stable under sensor perturbations.

A method to eliminate redundant coverage after perturbation is proposed.

The extended Rips interleaving theorem underpins the stability result.

Abstract

To the coverage problem of sensor networks, V. de Silva and R. Ghrist (2007) developed several approaches based on (persistent) homology theory. Their criteria for the coverage are formulated on the Rips complexes constructed by the sensors, in which their locations are supposed to be fixed. However, the sensors are in general affected by perturbations (e.g., natural phenomena), and hence the stability of the coverage criteria should be also discussed. In this paper, we present a coverage theorem stable under perturbation. Furthermore, we also introduce a method of eliminating redundant cover after perturbation. The coverage theorem is derived by extending the Rips interleaving theorem studied by F. Chazal, V. de Silva, and S. Oudot (2013) into an appropriate relative version.