TY - JOUR

T1 - Approximating the weight of the Euclidean minimum spanning tree in sublinear time

AU - Czumaj, Artur

AU - Ergün, Funda

AU - Fortnow, Lance

AU - Magen, Avner

AU - Newman, Ilan

AU - Rubinfeld, Ronitt

AU - Sohler, Christian

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Minimum spanning tree

KW - Sublinear algorithms

UR - http://www.scopus.com/inward/record.url?scp=33644586323&partnerID=8YFLogxK

U2 - 10.1137/S0097539703435297

DO - 10.1137/S0097539703435297

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AN - SCOPUS:33644586323

SN - 0097-5397

VL - 35

SP - 91

EP - 109

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 1

ER -