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Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance

MPS-Authors
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Bringmann,  Karl
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Künnemann,  Marvin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Nusser,  André
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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arXiv:1901.01504.pdf
(Preprint), 2MB

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Citation

Bringmann, K., Künnemann, M., & Nusser, A. (2019). Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance. Retrieved from http://arxiv.org/abs/1901.01504.


Cite as: http://hdl.handle.net/21.11116/0000-0005-3D76-3
Abstract
The Fr\'echet 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 Fr\'echet 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 Fr\'echet distance. The bottleneck of the top three implementations turned out to be precisely the decision procedure for the Fr\'echet distance. In this work, we present a fast, certifying implementation for deciding the Fr\'echet 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.