Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, October 09, 2008, 12:15 pm

**Duration**: This information is not available in the database

**Location**: OAT S15/S16/S17

**Speaker**: Martin Jaggi

*Core-sets* have proven to be a fruitful concept for
approximation algorithms in high-dimensional geometry.
The concept has initially been proposed for the smallest enclosing
ball problem for a set of points in R^{d}. Here an
*ε-core-set* is a subset of the points, such that the
smallest enclosing ball of the core-set, blown up by (1+ε),
encloses all the points.
It was shown that here core-sets of size as small as
^{⌈}1/ε^{⌉}
do exist, can be found quite easily,
and this is optimal. It is surprising (at least to me) that this size
is not only independent of the number of points, but also independent
of the dimension d.

In this talk I will try to translate these ideas to the *polytope
distance problem*, i.e. finding the point inside a polytope which
is closest to the origin. We will see that also in this setting,
Θ(1/ε) lower and upper bounds for the core-set size can
be established, thus also independent of dimension and number of
points.

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