Communication-efficient construction of the plane localized delaunay graph

Authors:
Prosenjit Bose;Paz Carmi;Michiel Smid;Daming Xu
Affiliations:
School of Computer Science, Carleton University, Ottawa, Canada;Department of Computer Science, Ben-Gurion University, Beer-Sheva, Israel;School of Computer Science, Carleton University, Ottawa, Canada;School of Computer Science, Carleton University, Ottawa, Canada
Venue:
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Year:
2010

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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 $\frac{4 \pi \sqrt{3}}{9}$-spanner of the unit-disk graph $\mathord{\it UDG}(V)$. Each node can only communicate with nodes that are within unit-distance from it. This algorithm only makes one round of communication and each point of V broadcasts at most 5 messages. This improves on all previously known message-bounds for this problem.