New applications of random sampling in computational geometry
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...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 methods in this paper
...The O(log s) query time of the algorithm given here is much faster that of several algorithms previously known [29, 30, 7]....
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...Recently systematic methods have been developed to apply such perturbations \formally," that is, to break ties in an arbitrary but consistent way, so as to simulate nondegeneracy with degenerate input [22, 44 ]....
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