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On the Average Performance of Orthogonal Range Search in Multidimensional Data Structures

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Automata, Languages and Programming (ICALP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2380))

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Abstract

In this work we present the average-case analysis of orthogonal range search for several multidimensional data structures. We first consider random relaxed K- d trees as a prototypical example. Later we extend these results to many different multidimensional data structures. We show that the performance of range searches is related to the performance of a variant of partial matches using a mixture of geometric and combinatorial arguments. This reduction simplifies the analysis and allows us to give exact lower and upper bounds for the performance of range searches. Furthermore, under suitable conditions ( “small range queries”), we can also get a very precise asymptotic estimate for the expected cost of range searches.

This research was supported by project DGES PB98-0926 (AEDRI) of the Spanish Ministery for Education and Science. The second author was also supported the Future and Emergent Technologies programme of the EU under contract IST-1999-14186 (ALCOM-FT).

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Author information

Authors and Affiliations

  1. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica deCatalunya, E-08034, Barcelona, Spain

    Amalia Duch & Conrado Martínez

  2. Laboratorio Nacional de Informática, Avanzada (LANIA), Xalapa, Mexico

    Amalia Duch & Conrado Martínez

Authors
  1. Amalia Duch
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  2. Conrado Martínez
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Editor information

Editors and Affiliations

  1. Institute of Theoretical Computer Science, ETH Zentrum, ETH Zürich, 8092, Zürich, Switzerland

    Peter Widmayer  & Stephan Eidenbenz  & 

  2. Department of Languages and Sciences of the Computation E.T.S. de Ingeniería Informática, University of Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Francisco Triguero , Rafael Morales  & Ricardo Conejo ,  & 

  3. School of Cognitive and Computing Sciences, University of Sussex, Falmer, Brighton, BN1 9QN, UK

    Matthew Hennessy

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© 2002 Springer-Verlag Berlin Heidelberg

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Duch, A., Martínez, C. (2002). On the Average Performance of Orthogonal Range Search in Multidimensional Data Structures. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_44

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  • DOI: https://doi.org/10.1007/3-540-45465-9_44

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43864-9

  • Online ISBN: 978-3-540-45465-6

  • eBook Packages: Springer Book Archive

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