Hierarchical neighbor graphs: A low stretch connected structure for points in Euclidean space

TL;DR

This paper introduces hierarchical neighbor graphs, a low-energy, scalable, and dynamically reconfigurable network structure for ad hoc wireless sensor networks that achieves low power stretch and compares favorably with existing models.

Contribution

It presents a novel hierarchical neighbor graph architecture that is easy to form, repair, and reconfigure, with low power stretch and constant expected degree, suitable for wireless sensor networks.

Findings

Achieves energy-efficient reorganization as battery depletes

Provides low power stretch close to direct connections

Has expected constant degree and requires minimal computation

Abstract

We introduce hierarchical neighbor graphs, a new architecture for connecting ad hoc wireless nodes distributed in a plane. The structure has the flavor of hierarchical clustering and requires only local knowledge and minimal computation at each node to be formed and repaired. Hence, it is a suitable interconnection model for an ad hoc wireless sensor network. The structure is able to use energy efficiently by reorganizing dynamically when the battery power of heavily utilized nodes degrades and is able to achieve throughput, energy efficiency and network lifetimes that compare favorably with the leading proposals for data collation in sensor networks such as LEACH (Heinzelman et. al., 2002). Additionally, hierarchical neighbor graphs have low power stretch i.e. the power required to connect nodes through the network is a small factor higher than the power required to connect them directly. Our structure also compares favorably to mathematical structures proposed for connecting points in a plane e.g. nearest-neighbor graphs (Ballister et. al., 2005), $\theta$-graphs (Ruppert and Seidel, 1991), in that it has expected constant degree and does not require any significant computation or global information to be formed.