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A Unified Approach to Approximate Proximity Searching

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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

The inability to answer proximity queries efficiently for spaces of dimension d > 2 has led to the study of approximation to proximity problems. Several techniques have been proposed to address different approximate proximity problems. In this paper, we present a new and unified approach to proximity searching, which provides efficient solutions for several problems: spherical range queries, idempotent spherical range queries, spherical emptiness queries, and nearest neighbor queries. In contrast to previous data structures, our approach is simple and easy to analyze, providing a clear picture of how to exploit the particular characteristics of each of these problems. As applications of our approach, we provide simple and practical data structures that match the best previous results up to logarithmic factors, as well as advanced data structures that improve over the best previous results for all aforementioned proximity problems.

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Author information

Authors and Affiliations

  1. Department of Computer Science, The Hong Kong University of Science and Technology, Hong Kong

    Sunil Arya

  2. Universidade Federal do Estado do Rio de Janeiro (Unirio), Brazil

    Guilherme D. da Fonseca

  3. Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park

    David M. Mount

Authors
  1. Sunil Arya
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  2. Guilherme D. da Fonseca
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  3. David M. Mount
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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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Arya, S., da Fonseca, G.D., Mount, D.M. (2010). A Unified Approach to Approximate Proximity Searching. 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_32

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  • DOI: https://doi.org/10.1007/978-3-642-15775-2_32

  • 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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