Voronoi diagram

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Voronoi diagram

(mathematics, graphics)
(After G. Voronoi) For a set S of points in the Euclidean plane, the partition Vor(S) of the plane into the voronoi polygons associated with the members of S. Vor(S) is the dual of the Delaunay triangulation of S.
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A drawback is that the solution is computed at the cells' center of the Voronoi partition and an additional interpolation step is required, if the solution is needed on the original Cartesian mesh.
The Voronoi partition associated with those seeds is constructed using a simple geometric algorithm.
When transportation cost is dominant, it can be better to have a nonhierarchical distribution setup in which demand is served by the nearest facility without distinguishing the required service-time windows, the service areas (Voronoi partitions) are of similar size, and the facilities are centrally located in their service areas.
Moreover, having Voronoi partitions as service areas may not be an efficient approach.