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 M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, December 06, 2007, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Andreas Razen

On the Number of Crossing-Free Geometric Graphs (Part I)

Let P be a set of n points in general position in the plane. We show that there is a constant eps > 0 such that a uniformly at random chosen crossing-free geometric graph on P contains in expectation at least a (1/2+eps)-fraction of the number of edges in a triangulation of P.

Hereby we derive (to our knowledge) the first non-trivial constant c>0 such that the number of crossing-free geometric graphs on P is at most c^n times more than the number of triangulations of P. By trivial we mean that the estimate clearly holds if we choose c such that c^n=2^M, where M is the number of edges in a triangulation of P. For a triangular convex hull of P, where M=3n-6, we obtain a constant c<7.98. As the previous upper bounds for the number of crossing-free geometric graphs on planar point sets were derived using the trivial 8^n factor, we can now slightly decrease this bound to O(343.11^n).

Joint work with Jack Snoeyink and Emo Welzl.

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

Previous talks by year:   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