Deviation Estimates for Extremal Relay Random Geometric Graphs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915234717892608 |
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| author | Ganesan, Ghurumuruhan |
| author_facet | Ganesan, Ghurumuruhan |
| contents | In this paper, we consider a deterministic graph~\(Γ\) drawn on the unit square with straight line segments as edges and connect vertices of~\(Γ\) 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~\(Γ.\) 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~\(L_n.\) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deviation Estimates for Extremal Relay Random Geometric Graphs Ganesan, Ghurumuruhan Probability In this paper, we consider a deterministic graph~\(Γ\) drawn on the unit square with straight line segments as edges and connect vertices of~\(Γ\) 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~\(Γ.\) 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~\(L_n.\) |
| title | Deviation Estimates for Extremal Relay Random Geometric Graphs |
| topic | Probability |
| url | https://arxiv.org/abs/2504.07000 |