Sublinear Approximation of Euclidean Minimum Spanning Tree

A. Magen, F. Ergun, C. Sohler, R. Rubinfeld, A. Czumaj, I. Newman, L. Fortnow, in: Proceedings of the 14th ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), 2003, pp. 813–822.

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We consider the problem of finding the weight of a Euclidean minimum spanning tree for a set of n points in ℝd. We focus on the situation when the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within 1 + ε using only \~{O}(√ poly(1/ε)) queries for constant d. The algorithm assumes that the input is supported by a minimal bounding cube enclosing it, by orthogonal range queries, and by cone approximate nearest neighbors queries.
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Proceedings of the 14th ACM-SIAM Symposium on Discrete Algorithms (SODA 2003)
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813–822
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Magen A, Ergun F, Sohler C, et al. Sublinear Approximation of Euclidean Minimum Spanning Tree. In: Proceedings of the 14th ACM-SIAM Symposium on Discrete Algorithms (SODA 2003). ; 2003:813–822.
Magen, A., Ergun, F., Sohler, C., Rubinfeld, R., Czumaj, A., Newman, I., & Fortnow, L. (2003). Sublinear Approximation of Euclidean Minimum Spanning Tree. In Proceedings of the 14th ACM-SIAM Symposium on Discrete Algorithms (SODA 2003) (pp. 813–822).
@inproceedings{Magen_Ergun_Sohler_Rubinfeld_Czumaj_Newman_Fortnow_2003, title={Sublinear Approximation of Euclidean Minimum Spanning Tree}, booktitle={Proceedings of the 14th ACM-SIAM Symposium on Discrete Algorithms (SODA 2003)}, author={Magen, Avner and Ergun, Funda and Sohler, Christian and Rubinfeld, Ronitt and Czumaj, Artur and Newman, Ilan and Fortnow, Lance}, year={2003}, pages={813–822} }
Magen, Avner, Funda Ergun, Christian Sohler, Ronitt Rubinfeld, Artur Czumaj, Ilan Newman, and Lance Fortnow. “Sublinear Approximation of Euclidean Minimum Spanning Tree.” In Proceedings of the 14th ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), 813–822, 2003.
A. Magen et al., “Sublinear Approximation of Euclidean Minimum Spanning Tree,” in Proceedings of the 14th ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), 2003, pp. 813–822.
Magen, Avner, et al. “Sublinear Approximation of Euclidean Minimum Spanning Tree.” Proceedings of the 14th ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), 2003, pp. 813–822.

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