Summary and Info
The Voronoi diagram of a set of sites is a partition of the plane into regions, one to each site, such that the region of each site contains all points of the plane that are closer to this site than to the other ones. Such partitions are of great importance to computer science and many other fields. The challenge is to compute Voronoi diagrams quickly. The problem is that their structure depends on the notion of distance and the sort of site. In this book the author proposes a unifying approach by introducing abstract Voronoi diagrams. These are based on the concept of bisecting curves, which are required to have some simple properties that are actually possessed by most bisectors of concrete Voronoi diagrams. Abstract Voronoi diagrams can be computed efficiently and there exists a worst-case efficient algorithm of divide-and-conquer type that applies to all abstract Voronoi diagrams satisfying a certain constraint. The author shows that this constraint is fulfilled by the concrete diagrams based on large classes of metrics in the plane.
More About the Author
Ralf Kleinmann (born March 13, 1971 in Cologne, Germany) is an American football player from Germany who played as a placeckicker for NFL Europe team Frankfurt Galaxy from 1995-2000 and 2003-2004. He also played briefly for the Tampa Bay Buccaneers in the 2003 preseason before being released in late August 2003.
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