improved upper bound on the stretch factor of delaunay triangulations
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 ? = 1.998, improving the previous best upper bound of 2.42 by Keil and Gutwin (1989).
delaunay triangulation spanners stretch factor/dilation/spanning ratio