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arXiv · 0809.2956

Communication-Efficient Construction of the Plane Localized Delaunay Graph

Prosenjit Bose·Paz Carmi·Michiel Smid·Daming Xu
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Abstract

Let $V$ be a finite set of points in the plane. We present a 2-local algorithm that constructs a plane $\frac{4 π\sqrt{3}}{9}$-spanner of the unit-disk graph $\UDG(V)$. This algorithm makes only one round of communication and each point of $V$ broadcasts at most 5 messages. This improves the previously best message-bound of 11 by Araújo and Rodrigues (Fast localized Delaunay triangulation, Lecture Notes in Computer Science, volume 3544, 2004).

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Prosenjit Bose, Paz Carmi, Michiel Smid, Daming Xu. 2008-09-17. Communication-Efficient Construction of the Plane Localized Delaunay Graph. https://arxiv.org/abs/0809.2956

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