New applications of random sampling in computational geometry
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Cites methods from "New applications of random sampling..."
...More recently, the Voronoi digram [21] has provided a useful tool in low- dimensional Euclidian settings { and Figure 1: vp-tree decomposition Figure 2: kd-tree decomposition the overall eld and outlook of Computational Geometry has yielded many interesting results such as those of [22, 23, 24, 25] and earlier [26]....
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"New applications of random sampling..." refers background in this paper
...A combinatorial question relevant to several algorithms [5, 6, 14] concerns the quantity...
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...As in [14], it is assumed without loss of generality that the sites are in general position, that is, no four are coplanar....
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...Some bounds are known for fk,2(s) [14][15]....
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"New applications of random sampling..." refers methods in this paper
...The results in this paper have been used in an algorithm for triangulating simple polygons[17], for small-dimensional linear and integer programming[13], for an optimal parallel algorithm for Voronoi diagrams[39], and in various combinatorial results on arrangements[ 15 ]....
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"New applications of random sampling..." refers background in this paper
...The new bound gk,3(s) = O(sk 2 log(8) s/(log log s)(6)) is less than the [8] bound for all but very large k, and much less dependent on k than the [5] bound....
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...and by [8], gk,3(sO(log r/r)) = O((sO(log r/r)) (2)k) = O(k(3)(log s)(2))....
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...Cole and others [8] showed that gk,3(s) = O(s (2)k), and Chazelle and Preparata [5] showed that gk,3(s) = O(sk (5))....
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