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Orthogonal Range Searching in Linear and Almost-Linear Space

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Algorithms and Data Structures (WADS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4619))

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Abstract

In this paper we describe space-efficient data structures for two-dimensional range searching problem.

We present a dynamic linear space data structure that supports orthogonal range reporting queries in O(logn + klogε n) time, where k is the size of the answer. Our data structure also supports emptiness and one-reporting queries in O(logn) time and thus achieves optimal time and space for this type of queries. In the case of integer point coordinates, we describe a static linear space data structure that supports range reporting queries in O(logn/loglogn + klogε n) time and emptiness and one-reporting queries in O(logn/loglogn) time. This is the first linear space data structure for these problems that achieves sub-logarithmic query time.

We also present a dynamic linear space data structure for range counting queries with O((logn/loglogn)2) time and a dynamic O(nlogn/loglogn) space data structure for semi-group range sum queries with query time O((logn/loglogn)2).

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Authors and Affiliations

  1. Department of Computer Science, University of Bonn,  

    Yakov Nekrich

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  1. Yakov Nekrich
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Frank Dehne Jörg-Rüdiger Sack Norbert Zeh

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Nekrich, Y. (2007). Orthogonal Range Searching in Linear and Almost-Linear Space. In: Dehne, F., Sack, JR., Zeh, N. (eds) Algorithms and Data Structures. WADS 2007. Lecture Notes in Computer Science, vol 4619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73951-7_3

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  • DOI: https://doi.org/10.1007/978-3-540-73951-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73948-7

  • Online ISBN: 978-3-540-73951-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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