How to group wireless nodes together?

TL;DR

This survey reviews methods for static grouping of planar wireless nodes, focusing on point processes, models like Nearest Neighbour and Lilypond, and introduces new bounds and metrics for cluster analysis.

Contribution

The paper provides a comprehensive survey of static grouping methods for wireless nodes, introduces bounds for generation number, and proposes the ancestor number metric for cluster analysis.

Findings

Bounds for the generation number are established.

The ancestor number metric aids in analyzing cluster size distribution.

Static clustering with larger groups remains challenging in point processes.

Abstract

This report presents a survey on how to group together in a static way planar nodes, that may belong to a wireless network (ad hoc or cellular). The aim is to identify appropriate methods that could also be applied for Point Processes. Specifically matching pairs and algorithms are initially discussed. Next, specifically for Point Processes, the Nearest Neighbour and Lilypond models are presented. Properties and results for the two models are stated. Original bounds are given for the value of the so-called generation number, which is related to the size of the nearest neighbour cluster. Finally, a variation of the nearest neighbour grouping is proposed and an original metric is introduced, named here the ancestor number. This is used to facilitate the analysis of the distribution of cluster size. Based on this certain related bounds are derived. The report and the analysis included show clearly the difficulty of working in point processes with static clusters of size greater than two, when these are defined by proximity criteria.