Approximating the weight of the Euclidean minimum spanning tree in sublinear time

Document Type

Article

Publication Date

3-7-2006

Abstract

We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in 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 + ε using only Õ(√n 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 neighbor queries. © 2005 Society for Industrial and Applied Mathematics.

Identifier

33644586323 (Scopus)

Publication Title

SIAM Journal on Computing

External Full Text Location

https://doi.org/10.1137/S0097539703435297

ISSN

00975397

First Page

91

Last Page

109

Issue

1

Volume

35

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