One-sided epsilon-approximants

Boris Bukh; Gabriel Nivasch

doi:10.1007/978-3-319-44479-6_12

One-sided epsilon-approximants

Boris Bukh, Gabriel Nivasch

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

2 Scopus citations

Abstract

Given a finite point set P⊂R^d, we call a multiset A a one-sided weak ε-approximant for P (with respect to convex sets), if |P∩C|/|P|-|A∩C|/|A|≤ε for every convex set C. We show that, in contrast with the usual (two-sided) weak ε-approximants, for every set P⊂R^d there exists a one-sided weak ε-approximant of size bounded by a function of ε and d.

Original language	English
Title of host publication	A Journey through Discrete Mathematics
Subtitle of host publication	A Tribute to Jiri Matousek
Pages	343-356
Number of pages	14
ISBN (Electronic)	9783319444796
DOIs	https://doi.org/10.1007/978-3-319-44479-6_12
State	Published - 1 Jan 2017

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One-sided epsilon-approximants

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