ɛ-nets and simplex range queries
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- Haussler, D. & Welzl, E. Discrete Comput Geom (1987) 2: 127. doi:10.1007/BF02187876
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These bounds are better than those previously published for alld≥2. Based on ideas due to Vapnik and Chervonenkis, we introduce the concept of an ɛ-net of a set of points for an abstract set of ranges and give sufficient conditions that a random sample is an ɛ-net with any desired probability. Using these results, we demonstrate how random samples can be used to build a partition-tree structure that achieves the above query time.