TY - GEN
T1 - Weak 1/r-nets for moving points
AU - Rok, Alexandre
AU - Smorodinsky, Shakhar
N1 - Funding Information:
Work was partially supported by Grant 1136/12 from the Israel Science Foundation Work by this author was partially supported by Swiss National Science Foundation Grants 200020144531 and 200021-137574.
Publisher Copyright:
© Alexandre Rok and Shakhar Smorodinsky.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - In this paper, we extend the weak 1/r-net theorem to a kinetic setting where the underlying set of points is moving polynomially with bounded description complexity. We establish that one can find a kinetic analog N of a weak 1/r-net of cardinality O(rd(d+1)/2 logd r) whose points are moving with coordinates that are rational functions with bounded description complexity. Moreover, each member of N has one polynomial coordinate.
AB - In this paper, we extend the weak 1/r-net theorem to a kinetic setting where the underlying set of points is moving polynomially with bounded description complexity. We establish that one can find a kinetic analog N of a weak 1/r-net of cardinality O(rd(d+1)/2 logd r) whose points are moving with coordinates that are rational functions with bounded description complexity. Moreover, each member of N has one polynomial coordinate.
KW - Hypergraphs
KW - Weak ε-nets
UR - http://www.scopus.com/inward/record.url?scp=84976871898&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.SoCG.2016.59
DO - 10.4230/LIPIcs.SoCG.2016.59
M3 - Conference contribution
AN - SCOPUS:84976871898
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 59.1-59.13
BT - 32nd International Symposium on Computational Geometry, SoCG 2016
A2 - Fekete, Sandor
A2 - Lubiw, Anna
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 32nd International Symposium on Computational Geometry, SoCG 2016
Y2 - 14 June 2016 through 17 June 2016
ER -