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- W4300486565 abstract "Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r in [0,1]$, we prove a new concentration result on the number of pairs of points of $P$ at a distance at most $r$ -- we show that this number lies in an interval that contains only $O(n log n)$ numbers. We also present simple linear time algorithms to construct the Delaunay triangulation, Euclidean MST, and the convex hull of the points of $P$. The MST algorithm is an interesting divide-and-conquer algorithm which might be of independent interest. We also provide a new proof that the expected complexity of the Delaunay triangulation of $P$ is linear -- the new proof is simpler and more direct, and might be of independent interest. Finally, we present a simple $tilde{O}(n^{4/3})$ time algorithm for the distance selection problem for $d=2$." @default.
- W4300486565 created "2022-10-03" @default.
- W4300486565 creator A5040577923 @default.
- W4300486565 creator A5091358318 @default.
- W4300486565 date "2022-08-07" @default.
- W4300486565 modified "2023-09-26" @default.
- W4300486565 title "Revisiting Random Points: Combinatorial Complexity and Algorithms" @default.
- W4300486565 doi "https://doi.org/10.48550/arxiv.2208.03829" @default.
- W4300486565 hasPublicationYear "2022" @default.
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