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Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance
[article]
2019
arXiv
pre-print
Preserved Fulltext
Still, fast practical implementations of the Fr\'echet distance, in particular for realistic input curves, are highly desirable. ...
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 ...
p:32 Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance This enables a wide range of future work. ...
arXiv:1901.01504v1
fatcat:whvk5waqzrdehnizsfkvwv2ew4
Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance
2019
International Symposium on Computational Geometry
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Still, fast practical implementations of the Fréchet distance, in particular for realistic input curves, are highly desirable. ...
In this work, we present a fast, certifying implementation for deciding the Fréchet distance, in order to (1) complement its pessimistic worst-case hardness by an empirical analysis on realistic input ...
S o C G 2 0 1 9 17: 14 914 Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance select a curve σ ∈ {σ 2 k , . . . , σ 2 k+1 −1 } uniformly at random 3 , compute the exact distance ...
doi:10.4230/lipics.socg.2019.17
dblp:conf/compgeom/BringmannKN19
fatcat:babazuu4ybfclpsbpvibtskvki
When Lipschitz Walks Your Dog: Algorithm Engineering of the Discrete Fréchet Distance under Translation
[article]
2020
arXiv
pre-print
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Spurred by the surprising performance of recent implementations for the Fréchet distance, we perform algorithm engineering for the Fréchet distance under translation. ...
For the related task of computing the distance value up to a desired precision, we engineer and compare different methods. ...
Conclusion We engineer the first practical implementation for the discrete Fréchet distance under translation in the plane. ...
arXiv:2008.07510v1
fatcat:fddnepz6vzcx5nu6yuobo2ersa
When Lipschitz Walks Your Dog: Algorithm Engineering of the Discrete Fréchet Distance Under Translation
2020
European Symposium on Algorithms
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Spurred by the surprising performance of recent implementations for the Fréchet distance, we perform algorithm engineering for the Fréchet distance under translation. ...
We believe that our implementation will enable, for the first time, the use of the Fréchet distance under translation in applications, whereas previous algorithmic approaches would have been computationally ...
Conclusion We engineer the first practical implementation for the discrete Fréchet distance under translation in the plane. ...
doi:10.4230/lipics.esa.2020.25
dblp:conf/esa/BringmannKN20
fatcat:26lwgipk6be7xla2rq3gt6q3u4
Walking the dog fast in practice: Algorithm engineering of the Fréchet distance
2021
Preserved Fulltext
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Still, fast practical implementations of the Fréchet distance, in particular for realistic input curves, are highly desirable. ...
In this work, we present a fast, certifying implementation for deciding the Fréchet distance, in order to (1) complement its pessimistic worst-case hardness by an empirical analysis on realistic input ...
We develop a fast, practical Fréchet distance implementation. ...
doi:10.20382/jocg.v12i1a4
fatcat:32np4gpyhne33gbt2sbu6geyvy
Cole's Parametric Search Technique Made Practical
[article]
2013
arXiv
pre-print
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In this paper, we provide an algorithm engineering framework that allows for the same asymptotic complexity to be achieved probabilistically in a way that is both simple and practical (i.e., suitable for ...
We show how this results in practical implementations of some geometric algorithms utilizing parametric searching and provide experimental results that prove practicality of the method. ...
A common explanation of the Fréchet distance between two curves, g and h, is the following: "A man is walking his dog. ...
arXiv:1306.3000v1
fatcat:cqofqytkhjelfdugslwgxhr6xu
A Practical Index Structure Supporting Fréchet Proximity Queries Among Trajectories
[article]
2020
arXiv
pre-print
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Based on clustering for metric indexes, we obtain a dynamic tree structure whose size is linear in the number of trajectories, regardless of the trajectory's individual sizes or the spatial dimension, ...
We present a scalable approach for range and k nearest neighbor queries under computationally expensive metrics, like the continuous Fréchet distance on trajectory data. ...
along \itP , and her dog, who walks monotonously along \itQ . ...
arXiv:2005.13773v1
fatcat:iaeevus3g5hc3ctcwqgjqyjp3u
Optimizing the Geometrical Accuracy of 2D Curvilinear Meshes
2014
Procedia Engineering
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The new distance is minimized through an unconstrained optimization procedure, allowing significant improvements of the geometrical accuracy of high order meshes. ...
The high order meshing procedure starts with a straight sided mesh. High order points are initially snapped to the real geometry without taking care of the validity of the high order elements. ...
Consider a man is walking with a dog on a leash. The man is walking on the one curve and the dog on the other one. Both may vary their speed that are represented by transformations α and β. ...
doi:10.1016/j.proeng.2014.10.386
fatcat:2dhzzznytfculmtgh3edz4yis4
Clustering Player Paths
2015
International Conference on Foundations of Digital Games
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Player traces can result in a vast amount of high-dimensional data. This information is crucial to game designers trying to understand player behaviour and for tailoring the game experience. ...
of cluster information. ...
ACKNOWLEDGEMENTS This research was supported by the Fonds de recherche du Québec -Nature et technologies, and the Natural Sciences and Engineering Research Council of Canada. ...
dblp:conf/fdg/CampbellTV15
fatcat:gfvh2dpos5envehwsv2ows4nzq
A GPU approach to subtrajectory clustering using the Fréchet distance
2012
Proceedings of the 20th International Conference on Advances in Geographic Information Systems - SIGSPATIAL '12
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This is to the best of our knowledge not only the first GPU implementation of a subtrajectory clustering algorithm but also the first implementation using the continuous Fréchet distance, instead of the ...
Given a trajectory T we study the problem of reporting all subtrajectory clusters of T . To measure similarity between curves we choose the Fréchet distance. ...
This is also known as the person-dog metric: imagine a person walking on f and a dog walking on g. ...
doi:10.1145/2424321.2424355
dblp:conf/gis/GudmundssonV12
fatcat:vym6lvsjrbeingnugspuqzcaua
A GPU Approach to Subtrajectory Clustering Using the Fréchet Distance
2015
IEEE Transactions on Parallel and Distributed Systems
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This is to the best of our knowledge not only the first GPU implementation of a subtrajectory clustering algorithm but also the first implementation using the continuous Fréchet distance, instead of the ...
Given a trajectory T we study the problem of reporting all subtrajectory clusters of T . To measure similarity between curves we choose the Fréchet distance. ...
This is also known as the person-dog metric: imagine a person walking on f and a dog walking on g. ...
doi:10.1109/tpds.2014.2317713
fatcat:4pawdhwdzrhyzgo5h5g7rrkcme
Optimizing the geometrical accuracy of curvilinear meshes
2016
Journal of Computational Physics
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2015 pre-print arXiv:1507.04052v1 fatcat:fcvfr4rjkfadrjinizc75zwjfu
A fast estimate of the geometrical accuracy, based on Taylor expansions of the curves, is introduced. ...
Standard measures of the distance between curves are considered to evaluate the geometrical accuracy in planar two-dimensional meshes, but they prove computationally too costly for optimization purposes ...
Acknowledgements This work has been partly funded by the European Commission under the FP7 grant "IDIHOM" (Industrialisation of High-Order Methods -A Top-Down Approach). ...
doi:10.1016/j.jcp.2016.01.023
fatcat:26hfxf3wevezhbhgbbucrml25a
The effect of GPS refresh rate on measuring police patrol in micro-places
2021
Crime Science
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AbstractWith the increasing prevalence of police interventions implemented in micro hot-spots of crime, the accuracy with which officer foot patrols can be measured is increasingly important for the robust ...
These results have significant implications for the measurement of police patrols in micro-places and evaluations of micro-place based interventions. ...
Acknowledgements The authors wish to thank the police forces involved and particularly the Metropolitan Police Service for their support in collecting the data used in this research. ...
doi:10.1186/s40163-021-00140-1
fatcat:3icwup3livge3av5fd5cvjjkd4
Approximating the integral Fréchet distance
2018
Computational geometry
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We present a pseudo-polynomial time (1+ε)-approximation algorithm for computing the integral and average Fréchet distance between two given polygonal curves T 1 and T 2 . ...
The running time is in O(ζ 4 n 4 /ε 2 ) where n is the complexity of T 1 and T 2 and ζ is the maximal ratio of the lengths of any pair of segments from T 1 and T 2 . ...
In the well-known dog-leash metaphor, the (standard) Fréchet distance is described as follows: suppose a person walks a dog, while both have to move from the starting point to the ending point on their ...
doi:10.1016/j.comgeo.2018.01.001
fatcat:d6maaooh3vhcdlndokdr6hr5li
Dynamic Time Warping Under Translation: Approximation Guided by Space-Filling Curves
[article]
2022
arXiv
pre-print
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However, like the Fréchet distance, the DTW distance is not invariant under translations. ...
For comparing polygonal curves π, σ in ℝ^d, it provides a robust, outlier-insensitive alternative to the Fréchet distance. ...
Acknowledgements We thank Christian Wulff-Nilsen for making us aware of an improved offline dynamic shortest paths data structure. ...
arXiv:2203.07898v2
fatcat:gxnpbeainjbipiixopvluvreke
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