TY - JOUR
T1 - Fast construction of nets in low-dimensional metrics and their applications
AU - Har-Peled, Sariel
AU - Mendel, Manor
PY - 2006
Y1 - 2006
N2 - We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: approximate nearest neighbor search, well-separated pair decomposition, spanner construction, compact representation scheme, doubling measure, and computation of the (approximate) Lipschitz constant of a function. In all cases, the running (preprocessing) time is near linear and the space being used is linear.
AB - We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: approximate nearest neighbor search, well-separated pair decomposition, spanner construction, compact representation scheme, doubling measure, and computation of the (approximate) Lipschitz constant of a function. In all cases, the running (preprocessing) time is near linear and the space being used is linear.
KW - Approximate distance oracle
KW - Distance labeling
KW - Doubling dimension
KW - Doubling measure
KW - Metric nets
KW - Nearest neighbor search
KW - Quadtree
UR - http://www.scopus.com/inward/record.url?scp=33749260659&partnerID=8YFLogxK
U2 - 10.1137/S0097539704446281
DO - 10.1137/S0097539704446281
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AN - SCOPUS:33749260659
SN - 0097-5397
VL - 35
SP - 1148
EP - 1184
JO - SIAM Journal on Computing
JF - SIAM Journal on Computing
IS - 5
ER -