Description
Abstract: Given a set S of n points in R^D, and an integer k such that 0 ≤ k < n, we show that a geometric graph with vertex set S, at most n − 1 + k edges, maximum degree five, and dilation O(n/(k + 1)) can be computed in time O(n log n). For any k, we also construct planar n-point sets for which any geometric graph with n − 1 + k edges has dilation Ω(n/(k + 1)); a slightly weaker statement holds if the points of S are required to be in convex position.
Joint work with Mark de Berg, Otfried Cheong, Joachim Gudmundsson, Herman Haverkort, Michiel Smid, Antoine Vigneron. Appeared in Computational Geometry: Theory and applications 40 (2008) 207–219.