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Testing Euclidean Spanners

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Algorithms – ESA 2010 (ESA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6346))

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Abstract

We develop a property testing algorithm with query complexity \(\tilde{\mathcal{O}}(\delta^{-5d} \epsilon^{-5} Dlog^6 \Delta\sqrt{n})\) that tests whether a directed geometric graph G = (P,E) with maximum degree D and vertex set P ⊆ {1,...,Δ}d (for constant d) is a Euclidean (1 + δ)-spanner. Such a property testing algorithm accepts every (1 + δ)-spanner and rejects with high constant probability every graph that is ε-far from this property, i.e., every graph that differs in more than ε|P| edges from every (1 + δ)-spanner.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Technische Universität Dortmund,  

    Frank Hellweg, Melanie Schmidt & Christian Sohler

Authors
  1. Frank Hellweg
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  2. Melanie Schmidt
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  3. Christian Sohler
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, TU Eindhoven, Eindhoven, The Netherlands

    Mark de Berg

  2. Institute for Computer Science, J.W. Goethe University, 60325, Frankfurt/Main, Germany

    Ulrich Meyer

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© 2010 Springer-Verlag Berlin Heidelberg

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Hellweg, F., Schmidt, M., Sohler, C. (2010). Testing Euclidean Spanners. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_6

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  • DOI: https://doi.org/10.1007/978-3-642-15775-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15774-5

  • Online ISBN: 978-3-642-15775-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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