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

Karl Bringmann, Marvin Künnemann, André Nusser
2019 arXiv   pre-print
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

Karl Bringmann, Marvin Künnemann, André Nusser, Michael Wagner
2019 International Symposium on Computational Geometry  
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]

Karl Bringmann, Marvin Künnemann, André Nusser
2020 arXiv   pre-print
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

Karl Bringmann, Marvin Künnemann, André Nusser, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
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

Karl Bringmann, Marvin Künnemann, André Nusser
2021
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]

Michael T. Goodrich, Paweł Pszona
2013 arXiv   pre-print
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]

Joachim Gudmundsson, Michael Horton, John Pfeifer, Martin P. Seybold
2020 arXiv   pre-print
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

Jean-François Remacle, Jonathan Lambrechts, Christophe Geuzaine, Thomas Toulorge
2014 Procedia Engineering  
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

Jonathan Campbell, Jonathan Tremblay, Clark Verbrugge
2015 International Conference on Foundations of Digital Games  
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

Joachim Gudmundsson, Nacho Valladares
2012 Proceedings of the 20th International Conference on Advances in Geographic Information Systems - SIGSPATIAL '12  
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

Joachim Gudmundsson, Nacho Valladares
2015 IEEE Transactions on Parallel and Distributed Systems  
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

Thomas Toulorge, Jonathan Lambrechts, Jean-François Remacle
2016 Journal of Computational Physics  
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

Oliver K. Hutt, Kate Bowers, Shane D. Johnson
2021 Crime Science  
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

Anil Maheshwari, Jörg-Rüdiger Sack, Christian Scheffer
2018 Computational geometry  
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]

Karl Bringmann, Sándor Kisfaludi-Bak, Marvin Künnemann, Dániel Marx, André Nusser
2022 arXiv   pre-print
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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