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An Efficient Query Algorithm for Trajectory Similarity Based on Fréchet Distance Threshold

Ning Guo, Mengyu Ma, Wei Xiong, Luo Chen, Ning Jing
2017 ISPRS International Journal of Geo-Information  
Demonstrated by experiments over real trajectory data in a multi-core hardware environment, the new algorithm shows favorable stability and scalability besides its higher efficiency in comparison with  ...  The algorithm is expedient to be implemented in parallel for further increases of speed.  ...  Abbreviations The following abbreviations are used in this manuscript: MPI Message Passing Interface OCJ Ordered Coverage Judgement MBR Minimum Boundary rectangle MPP Massively Parallel Processing  ... 
doi:10.3390/ijgi6110326 fatcat:laktapa5orhb3bhjsduwxvs2bm

Multi-resolution sketches and locality sensitive hashing for fast trajectory processing

Maria Astefanoaei, Paul Cesaretti, Panagiota Katsikouli, Mayank Goswami, Rik Sarkar
2018 Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems - SIGSPATIAL '18  
First, we obtain simple provable locality sensitive hash families for both the Hausdorff and Fréchet distance measures, useful in near neighbour queries.  ...  Second, we build a data structure called MRTS (Multi Resolution Trajectory Sketch), which contains sketches of varying degrees of detail.  ...  Now we turn to the other kinds of queries, and the data structure we use to solve them.  ... 
doi:10.1145/3274895.3274943 dblp:conf/gis/AstefanoaeiCKGS18 fatcat:bxgipgkjyfbmvhduljqrggywrq

Translation Invariant Fréchet Distance Queries [article]

Joachim Gudmundsson, André van Renssen, Zeinab Saeidi, Sampson Wong
2021 arXiv   pre-print
More specifically, we preprocess a trajectory in 𝒪(n^2 log^2 n) time and 𝒪(n^3/2) space, such that for any subtrajectory and any horizontal query segment we can compute their Translation Invariant Fréchet  ...  The query version, finding an optimal placement in the plane for a query segment where the Fréchet distance becomes minimized, is much less well understood.  ...  Querying the standard Fréchet distance between a given trajectory and a query trajectory has been studied [9, 10, 11, 13, 14] , but due to the difficult nature of the query problem, data structures only  ... 
arXiv:2102.05844v2 fatcat:ozcs7wg6l5a4hpe6nh4aildpie

Succinct Trit-array Trie for Scalable Trajectory Similarity Search [article]

Shunsuke Kanda, Koh Takeuchi, Keisuke Fujii, Yasuo Tabei
2020 arXiv   pre-print
We experimentally test tSTAT on its ability to retrieve similar trajectories for a query from large collections of trajectories and show that tSTAT performs superiorly in comparison to state-of-the-art  ...  on a tree data structure called trie.  ...  As in FRESH, multiple data structures according to the sketch length are built for efficient query retrievals.  ... 
arXiv:2005.10917v2 fatcat:bqozemq2knc5rjfyzpiwrguvle

A Practical Index Structure Supporting Fréchet Proximity Queries Among Trajectories [article]

Joachim Gudmundsson, Michael Horton, John Pfeifer, Martin P. Seybold
2020 arXiv   pre-print
We present a scalable approach for range and k nearest neighbor queries under computationally expensive metrics, like the continuous Fréchet distance on trajectory data.  ...  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,  ...  data structures to answer \itR NN queries under \delta F on trajectories in d = 2 dimensional space.  ... 
arXiv:2005.13773v1 fatcat:iaeevus3g5hc3ctcwqgjqyjp3u

Evaluating Distance Measures for Trajectories in the Mobile Setting

Nikolaos Larios, Christos Mitatakis, Vana Kalogeraki, Dimitrios Gunopulos
2015 International Conference on Machine Learning  
The algorithms for the measurement of the trajectory similarity have been implemented for mobile devices running Android OS. We evaluate our algorithms with real geospatial data.  ...  In this paper, we study algorithms in order to solve the problem of finding the most similar trajectory within a number of trajectories.  ...  Acknowledgements We would like to thank Demetris Zeinalipour-Yazti, "University of Cyprus" for his assistance by providing us the source code of the implementation of LCSS algorithm.  ... 
dblp:conf/icml/LariosMKG15 fatcat:5qdssfvcfvf5rfmle6ytkw7pqy

On the Approximate Nearest Neighbor Queries among Curves under the Fréchet Distance [article]

Majid Mirzanezhad
2021 arXiv   pre-print
In this paper, we revisit the problem and propose the first data structure for curves under the (continuous) Fréchet distance in ^d.  ...  We also revisit the time-window data structure for spatial density maps in [6].  ...  In the asymmetric case, we present a data structure of size O n such that for any polygonal query curve Q of size k answers the 5(1 + ε)δ-ANNS under the discrete Fréchet distance in O(kd) query time.  ... 
arXiv:2004.08444v2 fatcat:avtawlu3wzdyhjiz45d7lzxgte

Efficient trajectory queries under the Fréchet distance (GIS Cup)

Kevin Buchin, Yago Diez, Tom van Diggelen, Wouter Meulemans
2017 Proceedings of the 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems - SIGSPATIAL'17  
Consider a set P of trajectories (polygonal lines in R 2 ), and a query given by a trajectory Q and a threshold ε > 0.  ...  To answer the query, we wish to find all trajectories P ∈ P such that δ F (P, Q) ≤ ε, where δ F denotes the Fréchet distance.  ...  K.B. was supported in part by the Netherlands Organisation for Scientific Research (NWO, 612.001.207).  ... 
doi:10.1145/3139958.3140064 dblp:conf/gis/BuchinDDM17 fatcat:e4laefsejfc5daoposrp773ilm

REPOSE: Distributed Top-k Trajectory Similarity Search with Local Reference Point Tries [article]

Bolong Zheng, Lianggui Weng, Xi Zhao, Kai Zeng, Xiaofang Zhou, Christian S. Jensen
2021 arXiv   pre-print
We propose a distributed in-memory management framework called REPOSE for processing top-k trajectory similarity queries on Spark.  ...  We develop a reference point trie (RP-Trie) index to organize trajectory data for local search.  ...  Finally, for the Xi'an dataset, we set δ = 0.01 for Hausdorff, and δ = 0.03 for Frechet and DTW. We choose N p = 5 pivot trajectories. For queries, we use k = 100 as the default.  ... 
arXiv:2101.08929v2 fatcat:pt7nzqbnefasxnahkzwyigretq

FRESH: Fréchet Similarity with Hashing

Matteo Ceccarello and Anne Driemel and Francesco Silvestri
2019 arXiv   pre-print
This paper studies the r-range search problem for curves under the continuous Fréchet distance: given a dataset S of n polygonal curves and a threshold r>0, construct a data structure that, for any query  ...  We propose FRESH, an approximate and randomized approach for r-range search, that leverages on a locality sensitive hashing scheme for detecting candidate near neighbors of the query curve, and on a subsequent  ...  Vahrenhold for useful comments, and the developers of the UCR collection.  ... 
arXiv:1809.02350v3 fatcat:ciwiaam4inf2ndd2ryjybjnjpq

Detecting Commuting Patterns by Clustering Subtrajectories [chapter]

Kevin Buchin, Maike Buchin, Joachim Gudmundsson, Maarten Löffler, Jun Luo
2008 Lecture Notes in Computer Science  
In this paper we consider the problem of detecting commuting patterns in a trajectory. For this we search for similar subtrajectories.  ...  To measure spatial similarity we choose the Fréchet distance and the discrete Fréchet distance between subtrajectories, which are invariant under differences in speed.  ...  for the implementation.  ... 
doi:10.1007/978-3-540-92182-0_57 fatcat:haqj77ranvhkhecn4ruyqljsf4

DETECTING COMMUTING PATTERNS BY CLUSTERING SUBTRAJECTORIES

KEVIN BUCHIN, MAIKE BUCHIN, JOACHIM GUDMUNDSSON, MAARTEN LÖFFLER, JUN LUO
2011 International journal of computational geometry and applications  
In this paper we consider the problem of detecting commuting patterns in a trajectory. For this we search for similar subtrajectories.  ...  To measure spatial similarity we choose the Fréchet distance and the discrete Fréchet distance between subtrajectories, which are invariant under differences in speed.  ...  for the implementation.  ... 
doi:10.1142/s0218195911003652 fatcat:f2fvk5tbtbb6tdkhjleykaderq

Efficient and Effective Similar Subtrajectory Search with Deep Reinforcement Learning [article]

Zheng Wang, Cheng Long, Gao Cong, Yiding Liu
2020 arXiv   pre-print
despite that it could capture trajectory similarity in a finer-grained way and many applications take subtrajectories as basic units for analysis.  ...  However, the similar subtrajectory search (SimSub) problem, aiming to return a portion of a trajectory (i.e., a subtrajectory) which is the most similar to a query trajectory, has been mostly disregarded  ...  The authors would like to thank Eamonn Keogh for pointing out some references to the time series literature and also the anonymous reviewers for their constructive comments.  ... 
arXiv:2003.02542v2 fatcat:wupyxy3odremho5okuvg7ymolq

The Fréchet/Manhattan Distance and the Trajectory Anonymisation Problem [chapter]

Christof Ferreira Torres, Rolando Trujillo-Rasua
2016 Lecture Notes in Computer Science  
However, a trajectory may contain sensitive and private information, which raises the problem of whether spatio-temporal data can be published in a private manner.  ...  In this article, we introduce a novel distance measure for trajectories that captures both aspect of the microaggregation process, namely clustering and obfuscation.  ...  We show, through experiments on synthetic spatio-temporal data, that our approach outperforms previous comparable work in terms of utility. Outline of the paper. This paper is structured as follows.  ... 
doi:10.1007/978-3-319-41483-6_2 fatcat:ouspohgzm5ecfgwmusmgkb22wm

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  
to the near-neighbor data structure.  ...  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 Fréchet distance.  ...  To allow for a comparison with previous implementations (which are all in the query setting), we also run experiments with our decider plugged into a data structure for the query setting.  ... 
doi:10.4230/lipics.socg.2019.17 dblp:conf/compgeom/BringmannKN19 fatcat:babazuu4ybfclpsbpvibtskvki
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