Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time

A. Czumaj, F. Ergün, L. Fortnow, A. Magen, I. Newman, R. Rubinfeld, C. Sohler, SIAM Journal on Computing 35 (2005) 91–109.

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Abstract
We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in $\mathbb R^d$. We focus on the setting where 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 $1 + \eps$ using only $\widetilde{\O}(\sqrt{n} \, \text{poly} (1/\eps))$ 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 neighbor queries. Read More: https://epubs.siam.org/doi/10.1137/S0097539703435297
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Journal Title
SIAM Journal on Computing
Volume
35
Issue
1
Page
91-109
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Czumaj A, Ergün F, Fortnow L, et al. Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time. SIAM Journal on Computing. 2005;35(1):91-109. doi:10.1137/s0097539703435297
Czumaj, A., Ergün, F., Fortnow, L., Magen, A., Newman, I., Rubinfeld, R., & Sohler, C. (2005). Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time. SIAM Journal on Computing, 35(1), 91–109. https://doi.org/10.1137/s0097539703435297
@article{Czumaj_Ergün_Fortnow_Magen_Newman_Rubinfeld_Sohler_2005, title={Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time}, volume={35}, DOI={10.1137/s0097539703435297}, number={1}, journal={SIAM Journal on Computing}, author={Czumaj, Artur and Ergün, Funda and Fortnow, Lance and Magen, Avner and Newman, Ilan and Rubinfeld, Ronitt and Sohler, Christian}, year={2005}, pages={91–109} }
Czumaj, Artur, Funda Ergün, Lance Fortnow, Avner Magen, Ilan Newman, Ronitt Rubinfeld, and Christian Sohler. “Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time.” SIAM Journal on Computing 35, no. 1 (2005): 91–109. https://doi.org/10.1137/s0097539703435297.
A. Czumaj et al., “Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time,” SIAM Journal on Computing, vol. 35, no. 1, pp. 91–109, 2005.
Czumaj, Artur, et al. “Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time.” SIAM Journal on Computing, vol. 35, no. 1, 2005, pp. 91–109, doi:10.1137/s0097539703435297.

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