On Epsilon-Nets, Distance Oracles, and Metric Embeddings

Ilya Razenshteyn

On Epsilon-Nets, Distance Oracles, and Metric Embeddings

Data Structures and Algorithms 2012-06-20 v1 Combinatorics Metric Geometry

Authors: Ilya Razenshteyn

Abstract

We give two new applications of an observation from \cite{ADFGW11}. The first is an almost linear sized constant time data structure for reporting very large distances in undirected graphs. The second is a generic transformation of results about $\ell_1$ -embeddability of metrics to a setting, where we are interested in preservation of large distances only.

On Epsilon-Nets, Distance Oracles, and Metric Embeddings

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