## 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: Wednesday, July 05, 2006, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Csaba Dávid Tóth (Massachusetts Institute of Technology)

## Spanning Trees and Cuttings across Disks and Axis-Aligned Rectangles in Three-Space

Given $n$ points and a set of disjoint 2-dimensional {\em disk}s (barriers), we connect the points with a straight line spanning tree such that every disk cuts at most $O(\sqrt{n})$ edges of the tree. If the barriers are {\em axis-aligned rectangles}, then there is a straight line spanning tree such that every rectangle cuts only $O(n^{1/3})$ edges. Both bounds are best possible apart from constant factors. Our proofs crucially depend on new asymptotically tight bounds on {\em cuttings}: for disjoint disks in $\R^3$ and $r$, $1\leq r\leq n$, we construct a $\frac{1}{r}$-cutting of size $O(r^2)$. For axis-aligned rectangles in $\R^3$, we construct a $\frac{1}{r}$-cutting of size $O(r^{3/2})$.

Joint work with Eynat Rafalin and Diane Souvaine.

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