Sublinear-Time Approximation of Euclidean Minimum Spanning Tree (2003)
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BibTeX
@MISC{Czumaj03sublinear-timeapproximation,
author = {Artur Czumaj and Funda Ergün and Lance Fortnow and Avner Magen and Ilan Newman and Ronitt Rubinfeld and Christian Sohler},
title = {Sublinear-Time Approximation of Euclidean Minimum Spanning Tree},
year = {2003}
}
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Abstract
We consider the problem of estimating the weight of a Euclidean minimum spanning tree for a set of n points in R . 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. Our main result is that if we assume the access to the input is supported by a minimal bounding cube of the input, by orthogonal range queries, and by cone approximate nearest neighbors queries, then it is possible to estimate the weight of a Euclidean minimum spanning tree of P to within 1 + " using only e O( n poly(1=")) queries for constant d.
