Abstract
LetS be any set ofN points in the plane and let DT(S) be the graph of the Delaunay triangulation ofS. For all pointsa andb ofS, letd(a, b) be the Euclidean distance froma tob and let DT(a, b) be the length of the shortest path in DT(S) froma tob. We show that there is a constantc (≤((1+√5)/2) π≈5.08) independent ofS andN such that
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P. Chew, There is a planar graph almost as good as the complete graph,Proceedings of the Second Symposium on Computational Geometry, Yorktown Heights, NY, 1986, pp. 169–177.
T. Feder, personal communication, 1988.
F. P. Preparata and M. I. Shamos,Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.
P. Raghavan, personal communication, 1987.
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This research was supported in part by an AT&T Bell Laboratories Scholarship, by NSF Grants DMC-8451214, CCR87-00917, and CCR85-05517, and by a grant from the IBM Corporation.
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Dobkin, D.P., Friedman, S.J. & Supowit, K.J. Delaunay graphs are almost as good as complete graphs. Discrete Comput Geom 5, 399–407 (1990). https://doi.org/10.1007/BF02187801
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DOI: https://doi.org/10.1007/BF02187801