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: Thursday, May 29, 2008, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Gábor Fejes Tóth (Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary)

Shortest path among circles

Given a packing of open unit circles, any two points lying outside the circles at distance $d$ from one another can be connected by a path evading the circles and having length at most ${2\pi\over\sqrt{27}}(d-2)+\pi$. This bound cannot be improved for values of the form $2(k\sqrt3+1)$. Can a packing of incongruent circles with radii at most 1 force us to a greater detour? The answer is yes, but concerning this problem we have to be satisfied with weaker upper and lower bounds for the length of the shortest path.


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