On the Impact of Geometry on Ad Hoc Communication in Wireless Networks

TL;DR

This paper develops scalable, randomized broadcast algorithms for ad hoc wireless networks that do not depend on geometric location or network density, achieving efficient communication under the SINR model.

Contribution

It introduces new distributed coloring algorithms and broadcast protocols that operate without GPS info and are effective regardless of network density.

Findings

Broadcast in $O(D ext{log} n + ext{log}^2 n)$ rounds with all nodes active

Broadcast in $O(D ext{log}^2 n)$ rounds with spontaneous wake-up

Algorithms are based on a novel distributed coloring method

Abstract

In this work we address the question how important is the knowledge of geometric location and network density to the efficiency of (distributed) wireless communication in ad hoc networks. We study fundamental communication task of broadcast and develop well-scalable, randomized algorithms that do not rely on GPS information, and which efficiency formulas do not depend on how dense the geometric network is. We consider two settings: with and without spontaneous wake-up of nodes. In the former setting, in which all nodes start the protocol at the same time, our algorithm accomplishes broadcast in $O(D\log n + \log^2 n)$ rounds under the SINR model, with high probability (whp), where $D$ is the diameter of the communication graph and $n$ is the number of stations. In the latter setting, in which only the source node containing the original message is active in the beginning, we develop a slightly slower algorithm working in $O(D\log^2 n)$ rounds whp. Both algorithms are based on a novel distributed coloring method, which is of independent interest and potential applicability to other communication tasks under the SINR wireless model.