16th International Symposium on Algorithms and Computation, ISAAC 2005, pp.50 - 59
Abstract
Given a set S of n points in the plane, 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, and dilation O(n / (k + 1)) can be computed in time O(n log n). We also construct 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.
Publisher
16th International Symposium on Algorithms and Computation, ISAAC 2005