Abstract
Let S be a finite set of points in the Euclidean plane. Let D be a Delaunay triangulation of S. The stretch factor (also known as dilation or spanning ratio) of D is the maximum ratio, among all points p and q in S, of the shortest path distance from p to q in D over the Euclidean distance ||pq||. Proving a tight bound on the stretch factor of the Delaunay triangulation has been a long standing open problem in computational geometry.In this paper we prove that the stretch factor of the Delaunay triangulation of a set of points in the plane is less than ρ = 1.998, improving the previous best upper bound of 2.42 by Keil and Gutwin (1989).
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