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 -