Abstract
We give a deterministic O(<em>n</em> log <em>n</em>) sweepline algorithm to construct the generalized Voronoi diagram for n points in the plane or rather its dual the generalized Delaunay triangulation. The algorithm uses no transformations and it is developed solely from the sweepline paradigm together with greediness. A generalized Delaunay triangulation can be based on an arbitrary strictly convex Minkowski distance function (including all L_p distance functions 1 &lt; p &lt; *) in contrast to ordinary Delaunay triangualations which are based on the Euclidean distance function.
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