On the Stretch Factor of Convex Delaunay Graphs

Let C be a compact and convex set in the plane that contains the origin in its interior, and let S be a finite set of points in the plane. The Delaunay graph DGC (S) of S is defined to be the dual of the Voronoi diagram of S with respect to the convex distance function defined by C. We prove that DGC (S) is a t-spanner for S, for some constant t that depends only on the shape of the set C. Thus, for any two points p and q in S, the graph DGC (S) contains a path between p and q whose Euclidean length is at most t times the Euclidean distance between p and q.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Prosenjit Bose, Paz Carmi, Sébastien Collette, Michiel H. M. Smid
• Keywords: Convex Distance Function, CORR 2008, Delaunay Graph Dgc, Education, Voronoi Diagram