Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, March 22, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Andreas Razen

Transforming Spanning Trees

For a planar point set we consider the graph of crossing-free straight-line spanning trees where two spanning trees are adjacent if their union is crossing-free. Recently, it was shown that an upper bound on the diameter of this graph implies an upper bound on the diameter of the flip graph of pseudo-triangulations of the underlying point set.

We prove a lower bound of $\Omega( log(n) / log(log(n)) )$ for the diameter of the graph of spanning trees on a planar set of $n$ points. This almost matches the known upper bound of $O( log(n) )$. If we measure the diameter in terms of the number of convex layers $k$ of the point set, our lower bound construction is tight, i.e. the diameter is in $\Omega( log(k) )$ which matches the known upper bound of $O( log(k) )$. So far only constant lower bounds were known.

Joint work with Kevin Buchin, Takeaki Uno and Uli Wagner.

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