Encyclopedia of Algorithms

Editors: Ming-Yang Kao

Applications of Geometric Spanner Networks

2002; Gudmundsson, Levcopoulos, Narasimhan, Smid
  • Joachim Gudmundsson
  • Giri Narasimhan
  • Michiel Smid
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_15

Keywords and Synonyms

Stretch factor            

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 ℝd, then the notation |pq| is used to denote the Euclidean distance between p and q; the notation \( \delta_G(p,q) \)

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Recommended Reading

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Joachim Gudmundsson
    • 1
  • Giri Narasimhan
    • 2
  • Michiel Smid
    • 3
  1. 1.DMiSTNational ICT Australia LtdAlexandriaAustralia
  2. 2.School of Computing and Information ScienceFlorida International UniversityMiamiUSA
  3. 3.School of Computer ScienceCarleton UniversityOttawaCanada