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Encyclopedia of Algorithms pp 86–90Cite as

Applications of Geometric Spanner Networks

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  • First Online:

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Years and Authors of Summarized Original Work

  • 2002; Gudmundsson, Levcopoulos, Narasimhan, Smid

  • 2005; Gudmundsson, Narasimhan, Smid

  • 2008; Gudmundsson, Levcopoulos, Narasimhan, Smid

Problem Definition

Given a geometric graph in d-dimensional space, it is useful to preprocess it so that distance queries, exact or approximate, can be answered efficiently. Algorithms that can report distance queries in constant time are also referred to as “distance oracles.” With unlimited preprocessing time and space, it is clear that exact distance oracles can be easily designed. This entry sheds light on the design of approximate distance oracles with limited preprocessing time and space for the family of geometric graphs with constant dilation.

Notation and Definitions

If p and q are points in \(\mathcal{R}^{d}\), then the notation | pq | is used to denote the Euclidean distance between p and q; the notation δ G (p, q) is used to denote the Euclidean length of a shortest path between p and qin a...

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Author information

Authors and Affiliations

  1. DMiST, National ICT Australia Ltd, Alexandria, Australia

    Joachim Gudmundsson

  2. School of Information Technologies, University of Sydney, Sydney, NSW, Australia

    Joachim Gudmundsson

  3. Department of Computer Science, Florida International University, Miami, FL, USA

    Giri Narasimhan

  4. School of Computing and Information Sciences, Florida International University, Miami, FL, USA

    Giri Narasimhan

  5. School of Computer Science, Carleton University, Ottawa, ON, Canada

    Michiel Smid

Authors
  1. Joachim Gudmundsson
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  2. Giri Narasimhan
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  3. Michiel Smid
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Corresponding author

Correspondence to Joachim Gudmundsson .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Gudmundsson, J., Narasimhan, G., Smid, M. (2016). Applications of Geometric Spanner Networks. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_15

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