TL;DR
This paper demonstrates that beta-skeletons, including Gabriel graphs, can have arbitrarily large dilation, showing limitations in their efficiency for certain point set configurations.
Contribution
It provides a fractal construction proving unbounded dilation for all beta>0 in beta-skeletons, including Gabriel graphs.
Findings
Beta-skeletons can have arbitrarily large dilation.
This applies specifically to Gabriel graphs.
The result highlights limitations in beta-skeletons' efficiency.
Abstract
A fractal construction shows that, for any beta>0, the beta-skeleton of a point set can have arbitrarily large dilation. In particular this applies to the Gabriel graph.
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