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: Thursday, November 20, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Marek Sulovský

Circle containment problem

The question is intuitively the following: given a set of n points in the plane, can one always choose two points a, b from P such that every disk D containing a and b contains many points of P, i.e. |D \cap P| >= tn + o(n) for some constant t. What is the maximum value c of this constant?

Edelsbunner et al. proved in 1989 that c > 1/4.7 but the proof was quite long and even worse, not completely correct. Although the mistake was fixed by later papers of Lovász et al.'04 and independently by Abrego et al.'05 the resulting proof of the lower bound is still quite complicated.

I will present a recent very short proof of this bound by P. Ramos and R. Viana from this year [paper].

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