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- W1983660815 abstract "Consider the Delaunay triangulation T of a set P of points in the plane as a Euclidean graph, in which the weight of every edge is its length. It has long been conjectured that the dilation in T of any pair p, p in P, which is the ratio of the length of the shortest path from p to p' in T over the Euclidean distance ||pp'||, can be at most {pi}/2 approx 1.5708. In this paper, we show how to construct point sets in convex position with dilation > 1.5810 and in general position with dilation > 1.5846. Furthermore, we show that a sufficiently large set of points drawn independently from any distribution will in the limit approach the worst-case dilation for that distribution." @default.
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- W1983660815 date "2010-06-02" @default.
- W1983660815 modified "2023-09-27" @default.
- W1983660815 title "The dilation of the Delaunay triangulation is greater than π/2" @default.
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