Paper Info
Title
Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance.
Abstract
The Frechet distance provides a natural and intuitive measure for the popular task of computing the similarity of two (polygonal) curves. While a simple algorithm computes it in near-quadratic time, a strongly subquadratic algorithm cannot exist unless the Strong Exponential Time Hypothesis fails. Still, fast practical implementations of the Frechet distance, in particular for realistic input curves, are highly desirable. This has even lead to a designated competition, the ACM SIGSPATIAL GIS Cup 2017: Here, the challenge was to implement a near-neighbor data structure under the Frechet distance. The bottleneck of the top three implementations turned out to be precisely the decision procedure for the Frechet distance. In this work, we present a fast, certifying implementation for deciding the Frechet distance, in order to (1) complement its pessimistic worst-case hardness by an empirical analysis on realistic input data and to (2) improve the state of the art for the GIS Cup challenge. We experimentally evaluate our implementation on a large benchmark consisting of several data sets (including handwritten characters and GPS trajectories). Compared to the winning implementation of the GIS Cup, we obtain running time improvements of up to more than two orders of magnitude for the decision procedure and of up to a factor of 30 for queries to the near-neighbor data structure.
Year
Venue
DocType
2019
arXiv: Computational Geometry
Journal
Volume
Citations 
PageRank 
abs/1901.01504
0
0.34
References 
Authors
15
3
Name
Order
Citations
PageRank
Karl Bringmann142730.13
Marvin Künnemann29611.77
André Nusser373.34