Computing the Greedy Spanner in Near-Quadratic Time |
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Authors: | Prosenjit Bose Paz Carmi Mohammad Farshi Anil Maheshwari Michiel Smid |
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Affiliation: | 1. School of Computer Science, Carleton University, Ottawa, Ontario, K1S 5B6, Canada
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Abstract: | 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
O(n2logn)\ensuremath {\mathcal {O}}(n^{2}\log n)
time. Since computing the greedy spanner has an Ω(n
2) lower bound, the time complexity of our algorithm is optimal within a logarithmic factor. |
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Keywords: | |
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