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arXiv · 2504.07000

Deviation Estimates for Extremal Relay Random Geometric Graphs

Ghurumuruhan Ganesan
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Abstract

In this paper, we consider a deterministic graph~\(\Gamma\) drawn on the unit square with straight line segments as edges and connect vertices of~\(\Gamma\) using edges of a random geometric graph (RGG)~\(G\) with adjacency distance~\(r_n\) as relays. We call the resulting graph as a \emph{relay} RGG and determine sufficient conditions under such relay RGGs exist and are also near optimal, in terms of the graph parameters of~\(\Gamma.\) We then equip edges of~\(G\) with independent, exponentially distributed weights and obtain bounds for the maximum possible weight~\(W_n\) of a relay RGG with a given length~\(L_n.\)

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Ghurumuruhan Ganesan. 2025-04-09. Deviation Estimates for Extremal Relay Random Geometric Graphs. https://arxiv.org/abs/2504.07000

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