Abstract
Given any natural numberd, 0<ɛ<1, letf d (ɛ) denote the smallest integerf such that every range space of Vapnik-Chervonenkis dimensiond has anɛ-net of size at mostf. We solve a problem of Haussler and Welzl by showing that ifd≥2, then
Further, we prove thatf 1(ɛ)=max(2, ⌌ 1/ɛ ⌍−1), and similar bounds are established for some special classes of range spaces of Vapnik-Chervonenkis dimension three.
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Komlós, J., Pach, J. & Woeginger, G. Almost tight bounds forɛ-Nets. Discrete Comput Geom 7, 163–173 (1992). https://doi.org/10.1007/BF02187833
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DOI: https://doi.org/10.1007/BF02187833