Fast construction of nets in low dimensional metrics, and their applications

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.

• Type: Conference
• Year: 2005
• Where: COMPGEOM
• Authors: Sariel Har-Peled, Manor Mendel
• Keywords: COMPGEOM 2005, Constant Doubling Dimension, Discrete Geometry, Linear Time Algorithm, finite Metric Spaces