Static and Streaming Data Structures for Fréchet Distance Queries

Given a curve P with points in ℝ^d in a streaming fashion, and parameters ϵ > 0 and k, we construct a distance oracle that uses space, and given a query curve Q with k points in ℝ^d returns in time a 1+ϵ approximation of the discrete Fréchet distance between Q and P.In addition, we construct simplifications in the streaming model, oracle for distance queries to a sub-curve (in the static setting), and introduce the zoom-in problem. Our algorithms work in any dimension d, and therefore we generalize some useful tools and algorithms for curves under the discrete Fréchet distance to work efficiently in high dimensions.