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Computing the Greedy Spanner in Near-Quadratic Time

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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 \(\ensuremath {\mathcal {O}}(n^{2}\log n)\) 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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Authors and Affiliations

  1. School of Computer Science, Carleton University, Ottawa, Ontario, K1S 5B6, Canada

    Prosenjit Bose, Paz Carmi, Mohammad Farshi, Anil Maheshwari & Michiel Smid

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  1. Prosenjit Bose
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  2. Paz Carmi
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  3. Mohammad Farshi
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  4. Anil Maheshwari
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  5. Michiel Smid
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Corresponding author

Correspondence to Mohammad Farshi.

Additional information

An extended abstract of this paper appeared in the Proceedings of the 11th Scandinavian Workshop on Algorithm Theory (SWAT), Lecture Notes in Computer Science, vol. 5124, pp. 390–401, Springer, 2008.

Research supported in part by NSERC and MRI.

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Bose, P., Carmi, P., Farshi, M. et al. Computing the Greedy Spanner in Near-Quadratic Time. Algorithmica 58, 711–729 (2010). https://doi.org/10.1007/s00453-009-9293-4

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  • DOI: https://doi.org/10.1007/s00453-009-9293-4

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