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SODA
2001
ACM

Static and kinetic geometric spanners with applications

10 years 4 months ago
Static and kinetic geometric spanners with applications
It is well known that the Delaunay Triangulation is a spanner graph of its vertices. In this paper we show that any bounded aspect ratio triangulation in two and three dimensions is a spanner graph of its vertices as well. We extend the notion of spanner graphs to environments with obstacles and show that both the Constrained Delaunay Triangulation and bounded aspect ratio conforming triangulations are spanners with respect to the corresponding visibility graph. We also show how to kinetize the Constrained Delaunay Triangulation. Using such time-varying triangulations we describe how to maintain sets of near neighbors for a set of moving points in both unconstrained and constrained environments. Such nearest neighbor maintenance is needed in many virtual environments where nearby agents interact. Finally, we show how to use the Constrained Delaunay Triangulation in order to maintain the relative convex hull of a set of points moving inside a simple polygon.
Menelaos I. Karavelas, Leonidas J. Guibas
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2001
Where SODA
Authors Menelaos I. Karavelas, Leonidas J. Guibas
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