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

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

No Title


Blocking Light Rays

Chuanming Zong, Technische Universität Berlin

Let K be an n-dimensional convex body, Bn be the n-dimensional unit ball, and let l(K) be the minimal number of nonoverlapping translates of K which can block every light ray starting from K. To determine the values of l(Bn) is a well-known problem in Discrete Geometry. It was proposed and studied by Hornich and L. Fejes Tóth.

Recently, significant progresses have been achieved by Bárány, Böröczky, Henk, Soltan, Talata, and Zong. For example, it has been proved that there are two constants c and c' such that

\begin{displaymath}2^{cn}\le l(B_n)\le 2^{c'n}.\end{displaymath}

This talk will introduce their main methods and results.


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