Max-Planck-Institut für Informatik
max planck institut
informatik
mpii logo Minerva of the Max Planck Society
 

MPI-INF or MPI-SWS or Local Campus Event Calendar

<< Previous Entry Next Entry >> New Event Entry Edit this Entry Login to DB (to update, delete)
What and Who
Title:The discrepancy of jittered sampling
Speaker:Benjamin Doerr
coming from:Ecole Polytechnique, France
Speakers Bio:
Event Type:Talk
Visibility:D1, D2, D3, D4, D5, RG1, SWS, MMCI
We use this to send out email in the morning.
Level:AG Audience
Language:English
Date, Time and Location
Date:Wednesday, 3 August 2016
Time:11:00
Duration:30 Minutes
Location:Saarbr├╝cken
Building:E1 4
Room:024
Abstract
The geometric discrepancy problem asks for sets of N points evenly distributed in the d-dimensional unit cube [0,1)^d. Here "evenly distributed" means that ideally each axis-parallel rectangles R anchored in 0 contains $N \volume(R)$ points. It is not totally obvious that for this problem methods and thinking from discrete algorithmics are useful, but in a few recent works we were successfully following this road. For example, in 2013 we showed that a random point set usually leads to a rectangle R having $\sqrt{dN}$ points too many or too few, which provided a matching lower bound to the upper bounds of Heinrich et al. (2001) and Aistleitner (2011). In this work, we regard point set constructed from partitioning the unit cube into small cubes and putting exactly one point randomly into each cube. Again by using elementary combinatorial arguments, we determine the discrepancy of such point sets. Our result improves the recent upper and lower bounds of Steinerberger and Pausinger (2016) and disproves their guess on the true order of magnitude.
Contact
Name(s):Benjamin Doerr
Video Broadcast
Video Broadcast:NoTo Location:
Tags, Category, Keywords and additional notes
Note:
Attachments, File(s):
Created by:Benjamin Doerr, 08/01/2016 10:57 PMLast modified by:Uwe Brahm/MPII/DE, 11/24/2016 04:13 PM
  • Benjamin Doerr, 08/01/2016 11:02 PM
  • Benjamin Doerr, 08/01/2016 10:57 PM -- Created document.