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

Access to Document

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

Cite this

@inbook{2b18eade89fd4f5fa40529185e281a91,

title = "One-sided epsilon-approximants",

abstract = "Given a finite point set P⊂Rd, 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⊂Rd there exists a one-sided weak ε-approximant of size bounded by a function of ε and d.",

author = "Boris Bukh and Gabriel Nivasch",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.",

year = "2017",

month = jan,

day = "1",

doi = "10.1007/978-3-319-44479-6\_12",

language = "אנגלית",

isbn = "9783319444789",

pages = "343--356",

booktitle = "A Journey through Discrete Mathematics",

}

TY - CHAP

T1 - One-sided epsilon-approximants

AU - Bukh, Boris

AU - Nivasch, Gabriel

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Given a finite point set P⊂Rd, 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⊂Rd there exists a one-sided weak ε-approximant of size bounded by a function of ε and d.

AB - Given a finite point set P⊂Rd, 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⊂Rd there exists a one-sided weak ε-approximant of size bounded by a function of ε and d.

UR - https://www.scopus.com/pages/publications/85042460492

U2 - 10.1007/978-3-319-44479-6_12

DO - 10.1007/978-3-319-44479-6_12

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.chapter???

AN - SCOPUS:85042460492

SN - 9783319444789

SP - 343

EP - 356

BT - A Journey through Discrete Mathematics

ER -

One-sided epsilon-approximants

Abstract

Access to Document

Other files and links

Fingerprint

Cite this