English

Communication-Efficient Construction of the Plane Localized Delaunay Graph

Computational Geometry 2008-09-18 v1

Abstract

Let VV be a finite set of points in the plane. We present a 2-local algorithm that constructs a plane 4π39\frac{4 \pi \sqrt{3}}{9}-spanner of the unit-disk graph \UDG(V)\UDG(V). This algorithm makes only one round of communication and each point of VV 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).

Keywords

Cite

@article{arxiv.0809.2956,
  title  = {Communication-Efficient Construction of the Plane Localized Delaunay Graph},
  author = {Prosenjit Bose and Paz Carmi and Michiel Smid and Daming Xu},
  journal= {arXiv preprint arXiv:0809.2956},
  year   = {2008}
}
R2 v1 2026-06-21T11:21:13.026Z