@article{18855,
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
}},
author = {{Czumaj, Artur and Ergün, Funda and Fortnow, Lance and Magen, Avner and Newman, Ilan and Rubinfeld, Ronitt and Sohler, Christian}},
issn = {{0097-5397}},
journal = {{SIAM Journal on Computing}},
number = {{1}},
pages = {{91--109}},
title = {{{Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time}}},
doi = {{10.1137/s0097539703435297}},
volume = {{35}},
year = {{2005}},
}