Proximity Structures for Geometric Graphs

  • Sanjiv Kapoor
  • Xiang-Yang Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2748)


In this paper we study proximity structures like Delauney triangulations based on geometric graphs, i.e. graphs which are subgraphs of the complete geometric graph. Given an arbitrary geometric graph G, we define several restricted Voronoi diagrams, restricted Delaunay triangulations, relative neighborhood graphs, Gabriel graphs and then study their complexities when G is a general geometric graph or G is some special graph derived from the application area of wireless networks. Besides being of fundamental interest these structures have applications in topology control for wireless networks.


Planar Graph Transmission Range Minimum Span Tree Voronoi Diagram Delaunay Triangulation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Sanjiv Kapoor
    • 1
  • Xiang-Yang Li
    • 1
  1. 1.Department of Computer ScienceIllinois Institute of TechnologyChicagoUSA

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