Let V be a finite set of points in the plane. We present a 2-local algorithm that constructs a plane 4π √ 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 Araújo and Rodrigues (Fast localized Delaunay triangulation, Lecture Notes in Compute...

Abstract. Node overlap removal is a necessary step in many scenarios including laying out a graph, or visualizing a tag cloud. Our contribution is a new overlap removal algorithm that iteratively builds a Minimum Spanning Tree on a Delaunay triangulation of the node centers and removes the node overlaps by ”growing” the tree. The algorithm is simple to implement yet produces high quality layout...

We examine the problem of computing exactly the Delaunay graph of a set of possibly intersecting smooth convex pseudo-circles in the Euclidean plane given in parametric form. The diagram is constructed incrementally. We focus on InCircle, under the exact computation paradigm, and express it by a simple polynomial system, which allows for an efficient implementation by means of iterated resultan...

An important objective in the choice of a triangulation is that the smallest angle becomes as large as possible. In the straight line case, it is known that the Delaunay triangulation is optimal in this respect. We propose and study the concept of a circular arc triangulation— a simple and effective alternative that offers flexibility for additionally enlarging small angles—and discuss its appl...

We use here the results on the influence graph[1] to adapt them for particular cases where additional information is available. In some cases, it is possible to improve the expected randomized complexity of algorithms from O(n log n) to O(n log n). This technique applies in the following applications : triangulation of a simple polygon, skeleton of a simple polygon, Delaunay triangulation of po...

We study the problem of computing Voronoi diagrams distributedly for a set of nodes of a network modeled as a Unit Disk Graph (UDG). We present an algorithm to solve this problem efficiently, which has direct applications in wireless networks. Comparing with some existing algorithms, our algorithm correctly computes the complete Voronoi diagram and uses a significantly smaller number of transmi...

We use here the results on the in uence graph[1] to adapt them for particular cases where additional information is available. In some cases, it is possible to improve the expected randomized complexity of algorithms from O(n log n) to O(n log? n). This technique applies in the following applications : triangulation of a simple polygon, skeleton of a simple polygon, Delaunay triangulation of po...

| This article describes a topological routing path search algorithm embedded in our autorouter for printed circuit boards. The algorithm searches for a topological path that is guaranteed to be transformable into a physical wire satisfying design rules. We propose a method for incrementally verifying design rules during topological path search in a graph based on constrained Delaunay triangula...

A novel method for surface reconstruction from an unorganized point set is presented. An energy functional based on a weighted minimal surface model is proposed for surface reconstruction, which is efficiently minimized by graph cut methods. By solving the minimization problem on the graph dual to a Delaunaybased tetrahedral mesh, the advantages of explicit and implicit methods for surface reco...

Voronoi diagrams are a classical tool for analyzing spatial neighborhood relations. For point elds the spatial proximity can be easily visualized by the dual graph, the Delaunay triangulation. In image analysis VDs and DTs are commonly used to derive neighborhoods for grouping or for relational matching. Neighborhood relations derived from the VD, however, are uncertain in case the common side ...