Computing the Greedy Spanner in Near-Quadratic Time

AbstractThe greedy algorithm produces high-quality spanners and, therefore, is used in several applications. However, even for points in d-dimensional Euclidean space, the greedy algorithm has near-cubic running time. In this paper, we present an algorithm that computes the greedy spanner for a set of n points in a metric space with bounded doubling dimension in $\ensuremath {\mathcal {O}}(n^{2}\log n)$ time. Since computing the greedy spanner has an Ω(n2) lower bound, the time complexity of our algorithm is optimal within a logarithmic factor.

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