A novel wireless sensor network topology with fewer links

TL;DR

This paper introduces a new wireless sensor network topology based on a symmetric $(k,j)$-NN graph, which reduces the number of links needed for connectivity while maintaining high probability of network connectivity.

Contribution

The paper proposes a novel symmetric $(k,j)$-NN topology that selectively connects farthest neighbors, reducing links and improving efficiency in wireless sensor networks.

Findings

Connecting farthest $j$ neighbors among $k$ can ensure network connectivity.

More than 75% of links in a $k$-NN graph are unnecessary for connectivity.

A combined topology with $(k,j)$-NN and RGG is effective for constrained WSNs.

Abstract

This paper, based on $k$-NN graph, presents symmetric $(k,j)$-NN graph $(1 \leq j < k)$, a brand new topology which could be adopted by a series of network-based structures. We show that the $k$ nearest neighbors of a node exert disparate influence on guaranteeing network connectivity, and connections with the farthest $j$ ones among these $k$ neighbors are competent to build up a connected network, contrast to the current popular strategy of connecting all these $k$ neighbors. In particular, for a network with node amount $n$ up to $10^3$, as experiments demonstrate, connecting with the farthest three, rather than all, of the five nearest neighbor nodes, i.e. $(k,j)=(5,3)$, can guarantee the network connectivity in high probabilities. We further reveal that more than $0.75n$ links or edges in $5$-NN graph are not necessary for the connectivity. Moreover, a composite topology combining symmetric $(k,j)$-NN and random geometric graph (RGG) is constructed for constrained transmission radii in wireless sensor networks (WSNs) application.