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- W4287710505 abstract "In this paper we present new data structures for two extensively studied variants of the orthogonal range searching problem. First, we describe a data structure that supports two-dimensional orthogonal range minima queries in $O(n)$ space and $O(log^{varepsilon} n)$ time, where $n$ is the number of points in the data structure and $varepsilon$ is an arbitrarily small positive constant. Previously known linear-space solutions for this problem require $O(log^{1+varepsilon} n)$ (Chazelle, 1988) or $O(log nlog log n)$ time (Farzan et al., 2012). A modification of our data structure uses space $O(nlog log n)$ and supports range minima queries in time $O(log log n)$. Both results can be extended to support three-dimensional five-sided reporting queries. Next, we turn to the four-dimensional orthogonal range reporting problem and present a data structure that answers queries in optimal $O(log n/log log n + k)$ time, where $k$ is the number of points in the answer. This is the first data structure that achieves the optimal query time for this problem. Our results are obtained by exploiting the properties of three-dimensional shallow cuttings." @default.
- W4287710505 created "2022-07-26" @default.
- W4287710505 creator A5050513868 @default.
- W4287710505 date "2020-07-21" @default.
- W4287710505 modified "2023-10-17" @default.
- W4287710505 title "New Data Structures for Orthogonal Range Reporting and Range Minima Queries" @default.
- W4287710505 doi "https://doi.org/10.48550/arxiv.2007.11094" @default.
- W4287710505 hasPublicationYear "2020" @default.
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