TY - CHAP
T1 - One-sided epsilon-approximants
AU - Bukh, Boris
AU - Nivasch, Gabriel
N1 - Publisher Copyright:
© Springer International Publishing AG 2017.
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 - http://www.scopus.com/inward/record.url?scp=85042460492&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-44479-6_12
DO - 10.1007/978-3-319-44479-6_12
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AN - SCOPUS:85042460492
SN - 9783319444789
SP - 343
EP - 356
BT - A Journey through Discrete Mathematics
ER -