Static and Streaming Data Structures for Fréchet Distance Queries

07/21/2020
by   Arnold Filtser, et al.
0

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 O(1/ε)^kdlogε^-1 space, and given a query curve Q with k points in ℝ^d, returns in Õ(kd) 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/09/2019

Sublinear data structures for short Fréchet queries

We study metric data structures for curves in doubling spaces, such as t...
research
10/21/2018

Distributed Approximate Distance Oracles

Data structures that allow efficient distance estimation (distance oracl...
research
08/17/2023

Accelerating Aggregation Queries on Unstructured Streams of Data

Analysts and scientists are interested in querying streams of video, aud...
research
11/03/2020

Greedy k-Center from Noisy Distance Samples

We study a variant of the canonical k-center problem over a set of verti...
research
03/03/2022

Efficient Fréchet distance queries for segments

We study the problem of constructing a data structure that can store a t...
research
03/03/2020

About the Serpinsky-Knopp curve

The Serpinsky-Knopp curve is characterized as the only curve (up to isom...
research
02/16/2023

Detecting and approximating decision boundaries in low dimensional spaces

A method for detecting and approximating fault lines or surfaces, respec...

Please sign up or login with your details

Forgot password? Click here to reset