Spanners of additively weighted point sets

Authors:
Prosenjit Bose;Paz Carmi;Mathieu Couture
Affiliations:
School of Computer Science, Carleton University, Herzberg Building, 1125 Colonel By Drive, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Herzberg Building, 1125 Colonel By Drive, Ottawa, Ontario, Canada;School of Computer Science, Carleton University, Herzberg Building, 1125 Colonel By Drive, Ottawa, Ontario, Canada
Venue:
Journal of Discrete Algorithms
Year:
2011

Citing 5
Cited 0

Spatial tessellations: concepts and applications of Voronoi diagrams

Spatial tessellations: concepts and applications of Voronoi diagrams
Classes of graphs which approximate the complete Euclidean graph

Discrete & Computational Geometry
A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields

Journal of the ACM (JACM)
Computational geometry: algorithms and applications

Computational geometry: algorithms and applications
Geometric Spanner Networks

Geometric Spanner Networks

Quantified Score

Hi-index	0.01

Visualization

Abstract

We study the problem of computing geometric spanners for (additively) weighted point sets. A weighted point set is a set of pairs (p,r) where p is a point in the plane and r is a real number. The distance between two points (p"i,r"i) and (p"j,r"j) is defined as |p"ip"j|-r"i-r"j. We show that in the case where all r"i are positive numbers and |p"ip"j|=r"i+r"j for all i, j (in which case the points can be seen as non-intersecting disks in the plane), a variant of the Yao graph is a (1+@e)-spanner that has a linear number of edges. We also show that the Additively Weighted Delaunay graph (the face-dual of the Additively Weighted Voronoi diagram) has a spanning ratio bounded by a constant. The straight-line embedding of the Additively Weighted Delaunay graph may not be a plane graph. Given the Additively Weighted Delaunay graph, we show how to compute a plane straight-line embedding that also has a spanning ratio bounded by a constant in O(nlogn) time.