Sparse power-efficient topologies for wireless ad hoc sensor networks

TL;DR

This paper proposes sparse, power-efficient, and well-covered topologies for wireless ad hoc sensor networks that do not require full connectivity, enabling energy savings and effective routing.

Contribution

It introduces new subgraph constructions for geometric random graphs that are sparse, power-efficient, and easy to set up using local information.

Findings

Subgraph constructions are effective above certain parameter thresholds.

The topologies are sparse and maintain low graph distance.

A simple local routing algorithm is proposed.

Abstract

We study the problem of power-efficient routing for multihop wireless ad hoc sensor networks. The guiding insight of our work is that unlike an ad hoc wireless network, a wireless ad hoc sensor network does not require full connectivity among the nodes. As long as the sensing region is well covered by connected nodes, the network can perform its task. We consider two kinds of geometric random graphs as base interconnection structures: unit disk graphs $\UDG(2,\lambda)$ and $k$-nearest-neighbor graphs $\NN(2,k)$ built on points generated by a Poisson point process of density $\lambda$ in $\RR^2$. We provide subgraph constructions for these two models $\US(2,\lambda)$ and $\NS(2,k)$ and show that there are values $\lambda_s$ and $k_s$ above which these constructions have the following good properties: (i) they are sparse; (ii) they are power-efficient in the sense that the graph distance is no more than a constant times the Euclidean distance between any pair of points; (iii) they cover the space well; (iv) the subgraphs can be set up easily using local information at each node. We also describe a simple local algorithm for routing packets on these subgraphs. Our constructions also give new upper bounds for the critical values of the parameters $\lambda$ and $k$ for the models $\UDG(2,\lambda)$ and $\NN(2,k)$.