skip to main content
research-article

Error Bounded Line Simplification Algorithms for Trajectory Compression: An Experimental Evaluation

Published: 28 September 2021 Publication History

Abstract

Nowadays, various sensors are collecting, storing, and transmitting tremendous trajectory data, and it is well known that the storage, network bandwidth, and computing resources could be heavily wasted if raw trajectory data is directly adopted. Line simplification algorithms are effective approaches to attacking this issue by compressing a trajectory to a set of continuous line segments, and are commonly used in practice. In this article, we first classify the error bounded line simplification algorithms into different categories and review each category of algorithms. We then study the data aging problem of line simplification algorithms and distance metrics from the views of aging friendliness and aging errors. Finally, we present a systematic experimental evaluation of representative error bounded line simplification algorithms, including both compression optimal and sub-optimal methods, in terms of commonly adopted perpendicular Euclidean, synchronous Euclidean, and direction-aware distances. Using real-life trajectory datasets, we systematically evaluate and analyze the performance (compression ratio, average error, running time, aging friendliness, and query friendliness) of error bounded line simplification algorithms with respect to distance metrics, trajectory sizes, and error bounds. Our study provides a full picture of error bounded line simplification algorithms, which leads to guidelines on how to choose appropriate algorithms and distance metrics for practical applications.

References

[1]
Gill Barequet, Danny Z. Chen, Ovidiu Daescu, Michael T. Goodrich, and Jack Snoeyink. 2002. Efficiently approximating polygonal paths in three and higher dimensions. Algorithmica 33, 2 (2002), 150–167.
[2]
Hu Cao and Ouri Wolfson. 2005. Nonmaterialized motion information in transport networks. In Proceedings of the 10th international conference on Database Theory (ICDT’05).
[3]
Hu Cao, Ouri Wolfson, and Goce Trajcevski. 2006. Spatio-temporal data reduction with deterministic error bounds. VLDBJ 15, 3 (2006), 211–228.
[4]
W. Cao and Y. Li. 2017. DOTS: An online and near-optimal trajectory simplification algorithm. Journal of Systems and Software 126, Supplement C (2017), 34–44.
[5]
W. Chan and F. Chin. 1996. Approximation of polygonal curves with minimum number of line segments. IJCGA 6, 1 (1996), 378–387.
[6]
Danny Z. Chen and Ovidiu Daescu. 2002. Space-efficient algorithms for approximating polygonal curves in two dimensional space. IJCGA 13, 2 (2002), 95–111.
[7]
Minjie Chen, Mantao Xu, and Pasi Fränti. 2012. Compression of GPS trajectories. In Proceedings of the 2012 Data Compression Conference (DCC’12).
[8]
Minjie Chen, Mantao Xu, and Pasi Fränti. 2012. A fast multiresolution polygonal approximation algorithm for GPS trajectory simplification. TIP 21, 5 (2012), 2770–2785.
[9]
Yukun Chen, Kai Jiang, Yu Zheng, Chunping Li, and Nenghai Yu. 2009. Trajectory simplification method for location-based social networking services. In Proceedings of the 2009 International Workshop on Location Based Social Networks (LBSN’09).
[10]
Alminas Civilis, Christian S. Jensen, and Stardas Pakalnis. 2005. Techniques for efficient road-network-based tracking of moving objects. TKDE 17, 5 (2005), 698–712.
[11]
Ovidiu Daescu and Ningfang Mi. 2005. Polygonal chain approximation: A query based approach. Computational Geometry 30 (2005), 41–58.
[12]
David H. Douglas and Thomas K. Peucker. 1973. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Canadian Cartographer 10, 2 (1973), 112–122.
[13]
James George Dunham. 1986. Optimum uniform piecewise linear approximation of planar curves. TPAMI 8, 1 (1986), 67–75.
[14]
Hazem Elmeleegy, Ahmed K. Elmagarmid, Emmanuel Cecchet, Walid G. Aref, and Willy Zwaenepoel. 2009. Online piece-wise linear approximation of numerical streams with precision guarantees. PVLDB 2, 1 (2009), 145–156.
[15]
D. Eu and G. T. Toussaint. 1994. On approximation polygonal curves in two and three dimensions. CVGIP: Graphical Models and Image Processing 56, 3 (1994), 231–246.
[16]
Oliviu Ghica, Goce Trajcevski, Ouri Wolfson, Ugo Buy, Peter Scheuermann, Fan Zhou, and Dennis Vaccaro. 2010. Trajectory data reduction in wireless sensor networks. IJNGC 1, 1 (2010), 28–51.
[17]
Ranit Gotsman and Yaron Kanza. 2015. A dilution-matching-encoding compaction of trajectories over road networks. GeoInformatica 19, 2 (2015), 331–364.
[18]
Yunheng Han, Weiwei Sun, and Baihua Zheng. 2017. COMPRESS: A comprehensive framework of trajectory compression in road networks. TODS 42, 2 (2017), 11:1–11:49.
[19]
Henrik Hargitai, Jue Wang, Philip J. Stooke, Irina Karachevtseva, Akos Kereszturi, and Mátyás Gede. 2017. Map projections in planetary cartography. In Lecture Notes in Geoinformation and Cartography. Springer International Publishing.
[20]
John Hershberger and Jack Snoeyink. 1992. Speeding up the douglas-peucker line-simplification algorithm. Technical Report, University of British Columbia (1992).
[21]
Chih Chieh Hung, WenChih Peng, and WangChien Lee. 2015. Clustering and aggregating clues of trajectories for mining trajectory patterns and routes. VLDBJ 24, 2 (2015), 169–192.
[22]
Hiroshi Imai and Masao Iri. 1986. Computational-geometric methods for polygonal approximations of a curve. Computer Vision, Graphics, and Image Processing 36 (1986), 31–41.
[23]
Bingqing Ke, Jie Shao, and Dongxiang Zhang. 2017. An efficient online approach for direction-preserving trajectory simplification with interval bounds. In Proceedings of the 18th IEEE International Conference on Mobile Data Management (MDM’17).
[24]
Georgios Kellaris, Nikos Pelekis, and Yannis Theodoridis. 2013. Map-matched trajectory compression. Journal of Systems and Software 86 (2013), 1566–1579.
[25]
Eamonn J. Keogh, Selina Chu, David M. Hart, and Michael J. Pazzani. 2001. An online algorithm for segmenting time series. In Proceedings of the 2001 IEEE International Conference on Data Mining (ICDM’01).
[26]
Satoshi Koide, Yukihiro Tadokoro, Chuan Xiao, and Yoshiharu Ishikawa. 2018. CiNCT: Compression and retrieval for massive vehicular trajectories via relative movement labeling. In Proceedings of the 34th International Conference on Data Engineering (ICDE’18).
[27]
Ralph Lange, Frank Dürr, and Kurt Rothermel. 2011. Efficient real-time trajectory tracking. VLDBJ 20, 5 (2011), 671–694.
[28]
Tianyi Li, Ruikai Huang, Lu Chen, Christian S. Jensen, and Torben Bach Pedersen. 2020. Compression of uncertain trajectories in road networks. PVLDB 13, 7 (2020), 1050–1063.
[29]
Xuelian Lin, Jiahao Jiang, Shuai Ma, Yimeng Zuo, and Chunming Hu. 2019. One-pass trajectory simplification using the synchronous euclidean distance. VLDBJ 28, 6 (2019), 897–921.
[30]
Xuelian Lin, Shuai Ma, Han Zhang, Tianyu Wo, and Jinpeng Huai. 2017. One-pass error bounded trajectory simplification. PVLDB 10, 7 (2017), 841–852.
[31]
Jiajun Liu, Kun Zhao, Philipp Sommer, Shuo Shang, Brano Kusy, and Raja Jurdak. 2015. Bounded quadrant system: Error-bounded trajectory compression on the go. In Proceedings of the 31st International Conference on Data Engineering (ICDE’15).
[32]
Jiajun Liu, Kun Zhao, Philipp Sommer, Shuo Shang, Brano Kusy, Jae-Gil Lee, and Raja Jurdak. 2016. A novel framework for online amnesic trajectory compression in resource-constrained environments. TKDE 28, 11 (2016), 2827–2841.
[33]
Cheng Long, Raymond Chi-Wing Wong, and H. V. Jagadish. 2013. Direction-preserving trajectory simplification. PVLDB 6, 10 (2013), 949–960.
[34]
Cheng Long, Raymond Chi-Wing Wong, and H. V. Jagadish. 2014. Trajectory simplification: On minimizing the direction-based error. PVLDB 8, 1 (2014), 49–60.
[35]
Ge Luo, Ke Yi, Siu-Wing Cheng, Zhenguo Li, Wei Fan, Cheng He, and Yadong Mu. 2015. Piecewise linear approximation of streaming time series data with max-error guarantees. In Proceedings of the 31st International Conference on Data Engineering (ICDE’15).
[36]
R. Mariescu-Istodor and P. Fränti. 2017. Grid-based method for GPS route analysis for retrieval. ACM Transactions on Spatial Algorithms and Systems 3, 3 (2017), 1–28.
[37]
Jean Damascene Mazimpaka and Sabine Timpf. 2016. Trajectory data mining: A review of methods and applications. Journal of Spatial Information Science 13 (2016), 61–99.
[38]
Avraham Melkman and Joseph O’Rourke. 1988. On polygonal chain approximation. Machine Intelligence and Pattern Recognition 6 (1988), 87–95.
[39]
Nirvana Meratnia and Rolf A. de By. 2004. Spatiotemporal compression techniques for moving point objects. In Proceedings of the 9th International Conference on Extending Database Technology (EDBT’04).
[40]
Rohit Metha and V. K. Mehta. 1999. The Principles of Physics. S Chand.
[41]
Jonathan Muckell, Jeong-Hyon Hwang, Catherine T. Lawson, and S. S. Ravi. 2010. Algorithms for compressing GPS trajectory data: An empirical evaluation. In Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information (GIS’10).
[42]
Jonathan Muckell, Jeong-Hyon Hwang, Vikram Patil, Catherine T. Lawson, Fan Ping, and S. S. Ravi. 2011. SQUISH: An online approach for GPS trajectory compression. In Proceedings of the 2nd International Conference on Computing for Geospatial Research & Applications (COM.Geo’11).
[43]
Jonathan Muckell, Paul W. Olsen, Jeong-Hyon Hwang, Catherine T. Lawson, and S. S. Ravi. 2014. Compression of trajectory data: A comprehensive evaluation and new approach. GeoInformatica 18, 3 (2014), 435–460.
[44]
Aiden Nibali and Zhen He. 2015. Trajic: An effective compression system for trajectory data. TKDE 27, 11 (2015), 3138–3151.
[45]
Joseph O’Rourke. 1981. An on-line algorithm for fitting straight lines between data ranges. Communications of the ACM 24, 9 (1981), 574–578.
[46]
Theodosios Pavlidis and Steven L. Horowitz. 1974. Segmentation of plane curves. TOC 23, 8 (1974), 860–870.
[47]
Iulian Sandu Popa, Karine Zeitouni, Vincent Oria, and Ahmed Kharrat. 2014. Spatio-temporal compression of trajectories in road networks. GeoInformatica 19, 1 (2014), 117–145.
[48]
Michalis Potamias, Kostas Patroumpas, and Timos K. Sellis. 2006. Sampling trajectory streams with spatiotemporal criteria. In Proceedings of the 18th International Conference on Scientific and Statistical Database Management (SSDBM’06).
[49]
M. A. Quddus, W. Y. Ochieng, and R. B. Noland. 2007. Current map-matching algorithms for transport applications: State-of-the art and future research directions. Transportation Research Part C: Emerging Technologies 15, 5 (2007), 312–328.
[50]
U. Ramer. 1972. An iterative procedure for the polygonal approximation of plane curves. Computer Graphics and Image Processing 1 (1972), 244–256.
[51]
K. Reumann and A.P.M Witkam. 1974. Optimizing curve segmentation in computer graphics. In Proceedings of the 1973 International Computing Symposium.
[52]
Kai-Florian Richter, Falko Schmid, and Patrick Laube. 2012. Semantic trajectory compression: Representing urban movement in a nutshell. JOSIS 4, 1 (2012), 3–30.
[53]
Falko Schmid, Kai-Florian Richter, and Patrick Laube. 2009. Semantic trajectory compression. In International Symposium on Spatial and Temporal Databases (SSTD’09).
[54]
Wenzhong Shi and Chuikwan Cheung. 2006. Performance evaluation of line simplification algorithms for vector generalization. Cartographic Journal 43, 1 (2006), 27–44.
[55]
J. Sklansky and V. Gonzalez. 1980. Fast polygonal approximation of digitized curves. Pattern Recognition 12 (1980), 327–331.
[56]
Renchu Song, Weiwei Sun, Baihua Zheng, and Yu Zheng. 2014. PRESS: A novel framework of trajectory compression in road networks. PVLDB 7, 9 (2014), 661–672.
[57]
G. T. Toussaint. 1985. On the complexity of approximating polygonal curves in the plane. In International Symposium on Robotics and Automation.
[58]
Goce Trajcevski. 2016. Compression of spatio-temporal data – Advanced seminar. In Proceedings of the 17th IEEE International Conference on Mobile Data Management (MDM’16).
[59]
Goce Trajcevski, Hu Cao, Peter Scheuermanny, Ouri Wolfsonz, and Dennis Vaccaro. 2006. On-line data reduction and the quality of history in moving objects databases. In Proceedings of the 5th Acm International Workshop on Data Engineering for Wireless and Mobile Access (Mobide’06).
[60]
G. Trajcevski, O. Wolfson, K. Hinrichs, and S. Chamberlain. 2004. Managing uncertainty in moving objects databases. ACM Transactions on Database Systems (TODS) 29, 3 (2004), 463–507.
[61]
Robert Weibel. 1996. Generalization of spatial data: Principles and selected algorithms. Algorithmic Foundations of Geographic Information Systems, this book originated from the CISM Advanced School on the Algorithmic Foundations of Geographic Information Systems. 99–152.
[62]
Robert Weibel and Genevieve Dutton. 1999. Generalising spatial data and dealing with multiple representations. In Geographical Information Systems: Principles, Techniques, Management And Applications (2nd edition), Cambridge, Geoinformation International, P. A. Longley, M. F. Goodchild, D. J. Maquire, and R. W. Rhind (Eds). 125–155.
[63]
Charles M. Williams. 1978. An efficient algorithm for the piecewise linear approximation of planar curves. Computer Graphics and Image Processing 8 (1978), 286–293.
[64]
Charles M. Williams. 1981. Bounded straight-line approximation of digitized planar curves and lines. Computer Graphics and Image Processing 16 (1981), 370–381.
[65]
Qing Xie, Chaoyi Pang, Xiaofang Zhou, Xiangliang Zhang, and Ke Deng. 2014. Maximum error-bounded piecewise linear representation for online stream approximation. VLDBJ 23, 6 (2014), 915–937.
[66]
Dongxiang Zhang, Mengting Ding, Dingyu Yang, Yi Liu, Ju Fan, and Heng Tao Shen. 2018. Trajectory simplification: An experimental study and quality analysis. PVLDB 9, 11 (2018), 934–946.
[67]
Liangbin Zhao and Guoyou Shi. 2019. A trajectory clustering method based on Douglas-Peucker compression and density for marine traffic pattern recognition. Ocean Engineering 172 (2019), 456–467.
[68]
Zhiyuan Zhao and Alan Saalfeld. 1997. Linear-time sleeve-fitting polyline simplification algorithms. In Proceedings of AutoCarto 13.
[69]
Yu Zheng, Xing Xie, and Wei-Ying Ma. 2010. GeoLife: A collaborative social networking service among user, location and trajectory. IEEE Data Engineering Bulletin 33, 2 (2010), 32–39.

Cited By

View all
  • (2024)Line simplification with sidedness relationship consistency using the constrained total least squares methodTransactions in GIS10.1111/tgis.1315128:3(582-603)Online publication date: 26-Feb-2024
  • (2024)Collectively Simplifying Trajectories in a Database: A Query Accuracy Driven Approach2024 IEEE 40th International Conference on Data Engineering (ICDE)10.1109/ICDE60146.2024.00334(4383-4395)Online publication date: 13-May-2024
  • (2024)CMMTSE: Complex Road Network Map Matching Based on Trajectory Structure ExtractionApplied Intelligence10.1007/s10489-024-05751-054:24(12676-12696)Online publication date: 1-Dec-2024
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Database Systems
ACM Transactions on Database Systems  Volume 46, Issue 3
September 2021
172 pages
ISSN:0362-5915
EISSN:1557-4644
DOI:10.1145/3481695
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 September 2021
Accepted: 01 June 2021
Revised: 01 March 2021
Received: 01 April 2020
Published in TODS Volume 46, Issue 3

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. Trajectory compression
  2. line simplification
  3. batch algorithms
  4. online algorithms
  5. one-pass algorithms

Qualifiers

  • Research-article
  • Refereed

Funding Sources

  • National Key Research and Development Program
  • NSFC
  • SKLSDE

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)60
  • Downloads (Last 6 weeks)4
Reflects downloads up to 20 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2024)Line simplification with sidedness relationship consistency using the constrained total least squares methodTransactions in GIS10.1111/tgis.1315128:3(582-603)Online publication date: 26-Feb-2024
  • (2024)Collectively Simplifying Trajectories in a Database: A Query Accuracy Driven Approach2024 IEEE 40th International Conference on Data Engineering (ICDE)10.1109/ICDE60146.2024.00334(4383-4395)Online publication date: 13-May-2024
  • (2024)CMMTSE: Complex Road Network Map Matching Based on Trajectory Structure ExtractionApplied Intelligence10.1007/s10489-024-05751-054:24(12676-12696)Online publication date: 1-Dec-2024
  • (2024)PLMR: An Efficient Pre-trained Model for Aircraft Maneuver RecognitionBig Data and Security10.1007/978-981-97-4390-2_9(99-110)Online publication date: 21-Jul-2024
  • (2024)Representation with Minimized Max-Error in Optimal Piecewise Linear Approximation of Time Series DataWeb Information Systems Engineering – WISE 202410.1007/978-981-96-0579-8_10(133-147)Online publication date: 2-Dec-2024
  • (2023)VOLTCom: A Novel Online Trajectory Compression Method Based on Vector ProcessingIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2023.329494124:12(14982-14993)Online publication date: 28-Jul-2023
  • (2023)A Lightweight Framework for Fast Trajectory Simplification2023 IEEE 39th International Conference on Data Engineering (ICDE)10.1109/ICDE55515.2023.00184(2386-2399)Online publication date: Apr-2023
  • (2022)A trajectory data compression algorithm based on spatio-temporal characteristicsPeerJ Computer Science10.7717/peerj-cs.11128(e1112)Online publication date: 3-Oct-2022
  • (2022)Spatial Data Quality in the IoT Era: Management and ExploitationProceedings of the 2022 International Conference on Management of Data10.1145/3514221.3522568(2474-2482)Online publication date: 10-Jun-2022
  • (2022)Spatial Data Quality in the Internet of Things: Management, Exploitation, and ProspectsACM Computing Surveys10.1145/349833855:3(1-41)Online publication date: 3-Feb-2022
  • Show More Cited By

View Options

Login options

Full Access

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

HTML Format

View this article in HTML Format.

HTML Format

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media