Communication-Efficient Construction of the Plane Localized Delaunay Graph

Details Communication-Efficient Construction of the Plane Localized Delaunay Graph Communication-Efficient Construction of the Plane Localized Delaunay Graph

2008-09-17

arxiv.org/abs/0809.2956v1

Computer Science

Computational Geometry

Scientific paper

Let $V$ be a finite set of points in the plane. We present a 2-local algorithm that constructs a plane $\frac{4 \pi \sqrt{3}}{9}$-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 Ara\'{u}jo and Rodrigues (Fast localized Delaunay triangulation, Lecture Notes in Computer Science, volume 3544, 2004).

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