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External Memory Range Reporting on a Grid

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Algorithms and Computation (ISAAC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4835))

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Abstract

In this paper we present external memory data structures for orthogonal range reporting queries on a grid. Our data structure for two-dimensional orthogonal range reporting queries uses O((N/B)log2 N) blocks of space of size B and supports queries in optimal O(log2 log B U + T/B) time, where U is the size of universe, N is the number of elements in the data structure, and T is the size of the answer. Our data structure for three-sided range reporting queries that uses O(N/B) blocks of space and supports queries in O(log2 log B U + T/B) time. In the case of three-sided range reporting on a N×ℕ grid, we describe a \(O((N/B)\log^2_B N)\) space data structure with O(T/B) query time, a \(O((N/B)\log^*_B N)\) data structure with \(O(\log^*_B N +T/B)\) query time, and a O(N/B) space data structure with \(O(\log^{(k)}_B N +T/B)\) query time for any constant k.

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Authors and Affiliations

  1. Dept. of Computer Science, University of Bonn,  

    Yakov Nekrich

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  1. Yakov Nekrich
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Takeshi Tokuyama

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© 2007 Springer-Verlag Berlin Heidelberg

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Nekrich, Y. (2007). External Memory Range Reporting on a Grid. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_46

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  • DOI: https://doi.org/10.1007/978-3-540-77120-3_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77118-0

  • Online ISBN: 978-3-540-77120-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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