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: Tuesday, September 16, 2014, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Luis Barba (Carleton University / Université Libre de Bruxelles)

Detecting intersections between convex polyhedra

In this talk, we revisit the classic problem of preprocessing polyhedra independently so that given two preprocessed polyhedra $P$ and $Q$ in $R^d$ each translated and rotated, their intersection can be tested rapidly. For $d=3$ we show how to perform such a test in $O(\log |P| + \log |Q|)$ time after linear preprocessing time and space. This running time is the best possible and improves upon the last best known query time of $O(\log|P| \log|Q|)$ by Dobkin and Kirkpatrick (1990).

We then generalize this method to any constant dimension $d$, achieving the same optimal $O(\log |P| + \log |Q|)$ query time using a representation of size $O(|P|^{\lfloor d/2 \rfloor +\epsilon})$ for any $\epsilon > 0$ arbitrarily small. This answers an even older question posed by Dobkin and Kirkpatrick 30 years ago.


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