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

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 for polytope distance

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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