TY - JOUR
AB - 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
AU - Czumaj, Artur
AU - Ergün, Funda
AU - Fortnow, Lance
AU - Magen, Avner
AU - Newman, Ilan
AU - Rubinfeld, Ronitt
AU - Sohler, Christian
ID - 18855
IS - 1
JF - SIAM Journal on Computing
SN - 0097-5397
TI - Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time
VL - 35
ER -