Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, October 23, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Sonoko Moriyama (Tohoku University)

Holt-Klee condition on SEB cubes

The smallest enclosing ball problem (for short, the SEB problem) is known as one of classical problems of computational geometry. Given a set of n points in a d dimensional space, this problem is to find the d dimensional ball with the smallest radius which encloses all the n points of P. Szabo and Welzl in 2001 showed that if all the n points are affinely independent, the SEB problem is formulated as finding a unique sink on a unique sink orientation on an n-dimensional cube, called an SEB cube. There is another combinatorial condition defined on a unique sink orientation, Holt-Klee condition proposed by Holt and Klee in 1999. The Holt-Klee condition represents a directed version of the n-connectivity property of a unique sink orientation. In this talk, we prove that every SEB cube satisfies the Holt-Klee condition.

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