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On Spanners of Geometric Graphs

  • Conference paper
Theory and Applications of Models of Computation (TAMC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5532))

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Abstract

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.

The results in this paper are obtained jointly with Ljubmoir Perković and G. Xia.

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Author information

Authors and Affiliations

  1. School of Computing, DePaul University, 243 S. Wabash Ave., Chicago, IL 60604,  

    Iyad A. Kanj

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  1. Iyad A. Kanj
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Texas A&M University, College Station, 77843, Texas, USA

    Jianer Chen

  2. School of Mathematics, University of Leeds, LS2 9JT, U.K.

    S. Barry Cooper

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© 2009 Springer-Verlag Berlin Heidelberg

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Kanj, I.A. (2009). On Spanners of Geometric Graphs. In: Chen, J., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2009. Lecture Notes in Computer Science, vol 5532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02017-9_8

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  • DOI: https://doi.org/10.1007/978-3-642-02017-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02016-2

  • Online ISBN: 978-3-642-02017-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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