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33645739131
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rs, as the dissimilarity between configurations r and s and n the number of configurations. The need for diagonalization of B makes metric multidimensional scaling impractical on more than a few thousand configurations on current computers. However, additional points can be embedded in that space, using only dissimilarities to the points previously embedded (Ref. 33). The nature of the embedding will depend on which points were used to span the space; in an iterative procedure, it is conceivable to use either a diverse subset of points, leading to similar distortions for all points, or to use a representa-live subset, reducing the distortion in those regions which are most heavily populated.
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A space with a number of embedded points can be decomposed into cells, the Voronoi polyhedra, each comprising one point such that the space enclosed by a cell is closer to the corresponding point than to any other. A Delaunay diagram is the dual of its Voronoi diagram (see any textbook on Computational Geometry): every two points whose' Voronoi polyhedra share a face become Delaunay neighbors. If the points are nondegenerate, their Delaunay graph is a triangulation. Delaunay triangulations are optimal in the sense of avoiding long, skinny triangles.
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