Abstract
We present a data structure that supports three-dimensional range reporting queries in O(loglogU + (loglogn)3 + k) time and uses O(nlog1 + ε n) space, where U is the size of the universe, k is the number of points in the answer, and ε is an arbitrary constant. This result improves over the data structure of Alstrup, Brodal, and Rauhe (FOCS 2000) that uses O(nlog1 + ε n) space and supports queries in O(logn + k) time, the data structure of Nekrich (SoCG’07) that uses O(nlog3 n) space and supports queries in O(loglogU + (loglogn)2 + k) time, and the data structure of Afshani (ESA’08) that uses O(nlog3 n) space and also supports queries in O(loglogU + (loglogn)2 + k) time but relies on randomization during the preprocessing stage. Our result allows us to significantly reduce the space usage of the fastest previously known static and incremental d-dimensional data structures, d ≥ 3, at a cost of increasing the query time by a negligible O(loglogn) factor.
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Karpinski, M., Nekrich, Y. (2009). Space Efficient Multi-dimensional Range Reporting. In: Ngo, H.Q. (eds) Computing and Combinatorics. COCOON 2009. Lecture Notes in Computer Science, vol 5609. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02882-3_22
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DOI: https://doi.org/10.1007/978-3-642-02882-3_22
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