Abstract
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 \(\mathord{\it DG}_C(S)\) 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 \(\mathord{\it DG}_C(S)\) 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 \(\mathord{\it DG}_C(S)\) 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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Bose, P., Carmi, P., Collette, S., Smid, M. (2008). On the Stretch Factor of Convex Delaunay Graphs. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_58
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DOI: https://doi.org/10.1007/978-3-540-92182-0_58
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