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

__Mittagsseminar Talk Information__ | |

**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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