Randomized Incremental Construction of Delaunay and Voronoi Diagrams

In this paper we give a new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations. The new algorithm is more “online” than earlier similar methods, takes expected time O(n log n) and space O(n), and is eminently practical to implement. The analysis of the algorithm is also interesting in its own right and can serve as a model for many similar questions in both two and three dimensions. Finally we demonstrate how this approach for constructing Voronoi diagrams obviates the need for building a separate point-location structure for nearest-neighbor queries.

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