We consider the problem of computing spanners of Euclidean graphs embedded in the 2-dimensional Euclidean plane. We present an \(O(n\lg{n})\) time algorithm that computes a spanner of a Euclidean graph that is of bounded degree and plane, where n is the number of points in the graph. Both upper bounds on the degree and the stretch factor significantly improve the previous bounds. We extend this algorithm to compute a bounded-degree plane lightweight spanner of a Euclidean graph.

Our results rely on elegant structural and geometric results that we develop. Moreover, our results can be extended to Unit Disk graphs under the local distributed model of computation.


Delaunay Triangulation Geometric Graph Short Edge Span Subgraph Unit Disk Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Iyad A. Kanj
    • 1
  1. 1.School of ComputingDePaul UniversityChicago 

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