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On the stretch factor of convex delaunay graphs

par Bose, Prosenjit ;Carmi, Paz;Collette, Sébastien ;Smid, Michiel M.
Référence Lecture notes in computer science, 5369, page (665-667)
Publication Publié, 2008

Article révisé par les pairs

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Résumé :

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 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 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 contains a path between p and q whose Euclidean length is at most t times the Euclidean distance between p and q. © 2008 Springer Berlin Heidelberg.