Dynamic Random Geometric Graphs

TL;DR

This paper introduces Dynamic Random Geometric Graphs as a model for mobile wireless sensor networks, providing asymptotic analysis of connectivity periods and component probabilities at the connectivity threshold.

Contribution

It offers the first formal asymptotic results for connectivity dynamics in a basic model of mobile wireless sensor networks, extending static graph analysis.

Findings

Expected length of connectivity and disconnectivity periods derived

Asymptotic probabilities of component sizes at the connectivity threshold obtained

Formal tools developed for future studies in dynamic network models

Abstract

In this work we introduce Dynamic Random Geometric Graphs as a basic rough model for mobile wireless sensor networks, where communication distances are set to the known threshold for connectivity of static random geometric graphs. We provide precise asymptotic results for the expected length of the connectivity and disconnectivity periods of the network. We believe the formal tools developed in this work could be of use in future studies in more concrete settings. In addition, for static random geometric graphs at the threshold for connectivity, we provide asymptotic expressions on the probability of existence of components according to their sizes.