Extremal Properties of Three Dimensional Sensor Networks with Applications

TL;DR

This paper studies the critical thresholds for connectivity and coverage in three-dimensional sensor networks, analyzing phase transitions and proposing distributed protocols based on these properties.

Contribution

It provides a detailed analysis of phase transition thresholds for connectivity and coverage in 3D sensor networks and designs distributed algorithms based on these insights.

Findings

Identified critical sensing and transmission ranges for network connectivity.

Determined thresholds for coverage and degrees in 3D sensor deployments.

Proposed distributed protocols leveraging phase transition properties.

Abstract

In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a critical threshold, corresponding to the minimum amount of the communication effort or power expenditure by individual nodes, above (resp. below) which the property exists with high (resp. a low) probability. For sensor networks, properties of interest include simple and multiple degrees of connectivity/coverage. First, we investigate the network topology according to the region of deployment, the number of deployed sensors and their transmitting/sensing ranges. More specifically, we consider the following problems: Assume that $n$ nodes, each capable of sensing events within a radius of $r$, are randomly and uniformly distributed in a 3-dimensional region $\mathcal{R}$ of volume $V$, how large must the sensing range be to ensure a given degree of coverage of the region to monitor? For a given transmission range, what is the minimum (resp. maximum) degree of the network? What is then the typical hop-diameter of the underlying network? Next, we show how these results affect algorithmic aspects of the network by designing specific distributed protocols for sensor networks.