Application-layer multicast supports group applications without the need for a network-layer multicast protocol. Here, applications arrange themselves in a logical overlay network and transfer data within the overlay. In this paper, we present an application-layer multicast solution that uses a Delaunay triangulation as an overlay network topology. An advantage of using a Delaunay triangulation...

Several localized routing protocols [1] guarantee the delivery of the packets when the underlying network topology is the Delaunay triangulation of all wireless nodes. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we often model the network as a unit-disk graphUDG . In this paper, we present a novel localized networking ...

The restricted Delaunay triangulation is a subcomplex of the three-dimensional Delaunay triangulation that serves as a triangulation of a smooth surface embedded in three-dimensional space. It has proven itself as a mathematically powerful tool for surface meshing and surface reconstruction. I discuss two fascinating mathematical twists on these structures. First, I address a question of Bruno ...

Three-dimensional Delaunay triangulations are the most common form of three-dimensional triangulations known, but they are not very suitable for tetrahedral nite element meshes because they tend to contain poorly-shaped sliver tetrahedra. In this paper, we present an algorithm for constructing improved-quality triangulations with respect to a tetrahedron shape measure. This algorithm uses combi...

A triangulation of points in , or a tetrahedronization of points in , is used in many applications. It is not necessary to fulfill the Delaunay criteria in all cases. For large data (more then points), parallel methods are used for the purpose of decreasing time complexity. A new approach for fast and effective parallel CPU and GPU triangulation, or tetrahedronization, of large data sets in or ...

4 We show that Delaunay triangulations and compressed quadtrees are equivalent structures. More precisely, 5 we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay 6 triangulation; the second finds the Delaunay triangulation, given a compressed quadtree. Both algorithms 7 run in deterministic linear time on a pointer machine. Our work builds ...

Delaunay triangulations have been well-studied and numerous implementations have been proposed and instantiated over the years, but it was not until recently (2008) that a method for computing the Delaunay triangulation has been performed on the GPU. Even still, it was still presented as a hybrid method, utilizing the CPU in conjunction with the GPU. The dual of the Delaunay triangulation, the ...

Minimum spanning tree problem is a very important problem in VLSI CAD. Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least (n 2) time. More eecient approaches nd a minimum spanning tree only among edges in the Delaunay triangulation of the po...

Updating a Delaunay triangulation when its vertices move is a bottleneck in several domains of application. Rebuilding the whole triangulation from scratch is surprisingly a very viable option compared to relocating the vertices. This can be explained by several recent advances in efficient construction of Delaunay triangulations. However, when all points move with a small magnitude, or when on...

We propose two ways to compute the Delaunay triangulation of points on a sphere, or of rounded points close to a sphere, both based on the classic incremental algorithm initially designed for the plane. We use the so-called space of circles as mathematical background for this work. We present a fully robust implementation built upon existing generic algorithms provided by the cgal library. The ...