2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97239We 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, 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.41 pages. Extensive clean-up of minor English errorsData Structures and AlgorithmsComputational Geometrytext