A data structure for multi-dimensional range reporting

Authors:
Yakov Nekrich
Affiliations:
University of Bonn, Bonn, Germany
Venue:
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Year:
2007

Citing 14
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Abstract

We present a static data structure for orthogonal range reporting on a U x U x U integer grid. Our data structure supports orthogonal range reporting queries in O((log log n)2 + log log U + k) time and uses O(n log4 n) space, where k is the size of the answer. We describe a static data structure for range reporting in R4 with O(log nlog log n +k) query time and a static data structure for range reporting in Rd, d ≥ 5, with query time O((logd-3 n)/(log log n)d-5 +k). We also describe a semi-dynamic data structure that supports range reporting queries in R3 in O(log nlog log n +k) time and insertions in polylogarithmic time.