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Space Efficient Dynamic Orthogonal Range Reporting

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Abstract

In this paper we present new space efficient dynamic data structures for orthogonal range reporting. The described data structures support planar range reporting queries in time O(log n+klog log (4n/(k+1))) and space O(nlog log n), or in time O(log n+k) and space O(nlog ε n) for any ε>0. Both data structures can be constructed in O(nlog n) time and support insert and delete operations in amortized time O(log 2 n) and O(log nlog log n) respectively. These results match the corresponding upper space bounds of Chazelle (SIAM J. Comput. 17, 427–462, 1988) for the static case.

We also present a dynamic data structure for d-dimensional range reporting with search time O(log d−1 n+k), update time O(log d n), and space O(nlog d−2+ε n) for any ε>0.

The model of computation used in our paper is a unit cost RAM with word size log n.

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Authors and Affiliations

  1. Dept. of Computer Science, University of Bonn, Römerstrasse 164, 53117, Bonn, Germany

    Y. Nekrich

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  1. Y. Nekrich
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Correspondence to Y. Nekrich.

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A preliminary version of this paper appeared in the Proceedings of the 21st Annual ACM Symposium on Computational Geometry 2005.

Work partially supported by IST grant 14036 (RAND-APX).

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Nekrich, Y. Space Efficient Dynamic Orthogonal Range Reporting. Algorithmica 49, 94–108 (2007). https://doi.org/10.1007/s00453-007-9030-9

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