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 J. Lengler, A. Steger, and D. Steurer)

Mittagsseminar Talk Information

Date and Time: Tuesday, March 04, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Marek Sulovský

Circle containment problem and centerpoints

The following problem was posed at last year's GWOP:

What is the maximum c such that for every point set S in the plane, one can find a pair of points p, q with the property, that every disc D containing both p and q contains at least a c-fraction of the whole S (i.e. D intersected with S has size at least c|S|). This problem also has a natural higher dimensional generalization.

This question was first asked by Urrutia and Neuman-Lara in 1988 and there was some research on it in 1988-1989 but since then it did not receive any attention.

We improve the constant c for the high dimensional problem and relate it to some questions concerning so called lower center regions. The main argument involves Clarkson-Shor random sampling method combined with some bounds on the numbers of k-sets.

Warning: Since we use many basic geometric concepts and geometry backgrounds of the mittagsseminarists varies a lot, I will rather assume no particular knowledge. This means that I will spend quite o lot of time explaining basics like centerpoints and lifting map - my apology to all of you familiar with these concepts.

Joint work with Shakhar Smorodinsky and Uli Wagner. Special thanks to Jozsef Solymosi and Patrick Traxler.


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