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

Date and Time: Tuesday, April 25, 2006, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Jiří Matoušek (Charles Univ., Prague)

Zone diagrams

A zone diagram is a new variation of the classical notion of Voronoi diagram. Given points (sites) p_1,...,p_n in the plane, each p_i is assigned a region R_i, but in contrast to the ordinary Voronoi diagrams, the union of the R_i has a nonempty complement, the neutral zone. The defining property is that each R_i consists of all points that lie closer (non-strictly) to p_i than to the union of all the other R_j. Thus, the zone diagram is defined implicitly, by a fixed-point property, and neither its existence nor its uniqueness seem obvious. We prove both, as well as convergence of a natural iterative algorithm for computing it. Many challenging questions remain open.

Joint work with Tetsuo Asano and Takeshi Tokuyama.

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