A sparse graph almost as good as the complete graph on points in K dimensions
Discrete & Computational Geometry
Sparse geometric graphs with small dilation
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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An O(n log n)--time algorithm is presented that, when given a set S of n points in Rd and an integer k with 0 ≤ k ≤ n, computes a graph with vertex set S, that contains at most n − 1 + k edges, has stretch factor O(n/(k+1)), and whose degree is at most five. This generalizes a recent result of Aronov et al., who obtained this result for two-dimensional point sets.