Optimal one-dimensional coverage by unreliable sensors

TL;DR

This paper studies optimal placement strategies for unreliable sensors in a one-dimensional space, focusing on minimizing expected coverage gaps while accounting for sensor failure probabilities.

Contribution

It introduces a computational method for optimal sensor placement under failure probabilities and compares equispaced and random placements, proving asymptotic optimality of equispaced arrangements.

Findings

Equispaced placement becomes asymptotically optimal as sensor count increases.

Random placement has a strictly higher cost than equispaced placement.

The paper provides a method to compute optimal sensor configurations.

Abstract

This paper regards the problem of optimally placing unreliable sensors in a one-dimensional environment. We assume that sensors can fail with a certain probability and we minimize the expected maximum distance from any point in the environment to the closest active sensor. We provide a computational method to find the optimal placement and we estimate the relative quality of equispaced and random placements. We prove that the former is asymptotically equivalent to the optimal placement when the number of sensors goes to infinity, with a cost ratio converging to 1, while the cost of the latter remains strictly larger.