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The greedy spanner is a high-quality spanner: its total weight, edge count and maximal degree are asymptotically optimal and in practice significantly better than for any other spanner with reasonable construction time. Unfortunately, all known algorithms that compute the greedy spanner on $$n$$ n points use $$\varOmega (n^2)$$ Ω ( n 2 ) space, which is impractical on large instances...
The 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 $\ensuremath {\mathcal {O}}(n^{2}\log n)$...
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