Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, December 06, 2011, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Gabriel Nivasch (EPFL)

Upper bounds for centerflats

For every fixed d and every n, we construct an n-point set G in Rd such that every line in Rd is contained in a halfspace that contains only 2n/(d+2) points of G (up to lower-order terms).

Apparently, the point set G satisfies the following more general property: For every k, every k-flat in Rd is contained in a halfspace that contains only (k+1) n / (d+k+1) points of G (up to lower-order terms).

In 2008, Bukh, Matousek, and Nivasch conjectured the following generalization of Rado's centerpoint theorem: For every n-point set S in Rd and every k, there exists a k-flat f in Rd such that every halfspace that contains f contains at least (k+1) n / (d+k+1) points of S (up to lower-order terms). (The centerpoint theorem is obtained by setting k=0.) Such a flat f would be called a "centerflat".

Thus, our upper bound construction shows that the leading constant (k+1)/(k+d+1) in the above conjecture is tight (certainly for k = 1, and apparently for all k).

The set G of our construction is the "stretched grid" -- a point set which has been previously used by Bukh et al. for other related purposes.

Joint work with Boris Bukh.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login