On the stretch factor of convex Delaunay graphs

Prosenjit Bose, Paz Carmi, Sebastien Collette, Michiel Smid


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.

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DOI: http://dx.doi.org/10.20382/jocg.v1i1a4

ISSN: 1920-180X