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

Date and Time: Friday, July 05, 2002, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Mordecai J. Golin (Hong Kong University of Science and Technology)

The Probabilistic Complexity of the Voronoi Diagram of Points on a Polyhedron

It is well known that the complexity, i.e., the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as Theta(n^2). Interest has recently arisen as to what happens, both in deterministic and probabilistic situations, when the 3-dimensional points are restricted to lie on the surface of a 2-dimensional object. In this talk we consider the situation when the points are drawn from a 2-dimensional Poisson distribution with rate n over the surface of a polyhedron in 3-space. We show that with high probability the complexity of their Voronoi diagram is close is n polylog(n). This is joint work with Hyeonsuk Na.

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