2004
DOI: 10.1007/s00454-004-1116-4
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Abstract: Abstract. A finite set N ⊂ Rd is a weak ε-net for an n-point set X ⊂ R d (with respect to convex sets) if N intersects every convex set K with |K ∩ X | ≥ εn. We give an alternative, and arguably simpler, proof of the fact, first shown by Chazelle et al. [8], that every point set X in R d admits a weak ε-net of cardinality O(ε −d polylog(1/ε)). Moreover, for a number of special point sets (e.g., for points on the moment curve), our method gives substantially better bounds. The construction yields an algorithm …

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