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Fréchet Edit Distance

Authors Emily Fox, Amir Nayyeri, Jonathan James Perry , Benjamin Raichel

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  • Theory of computation → Computational geometry
Keywords
  • Fréchet distance
  • Edit distance
  • Hardness

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Abstract

We define and investigate the Fréchet edit distance problem. Given two polygonal curves π and σ and a threshhold value δ > 0, we seek the minimum number of edits to σ such that the Fréchet distance between the edited σ and π is at most δ. For the edit operations we consider three cases, namely, deletion of vertices, insertion of vertices, or both. For this basic problem we consider a number of variants. Specifically, we provide polynomial time algorithms for both discrete and continuous Fréchet edit distance variants, as well as hardness results for weak Fréchet edit distance variants.

Cite As Get BibTex

Emily Fox, Amir Nayyeri, Jonathan James Perry, and Benjamin Raichel. Fréchet Edit Distance. In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 58:1-58:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SoCG.2024.58

Author Details

Emily Fox
  • Department of Computer Science, University of Texas at Dallas, TX, USA
Amir Nayyeri
  • School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR, USA
Jonathan James Perry
  • Department of Computer Science, University of Texas at Dallas, TX, USA
Benjamin Raichel
  • Department of Computer Science, University of Texas at Dallas, TX, USA

Funding

  • Fox, Emily: Work on this paper was partially supported by NSF CAREER Award 1942597 and CCF Award 2311179.
  • Nayyeri, Amir: Work on this paper was partially supported by NSF Awards CCF 2311180 and CCF 1941086.
  • Perry, Jonathan James: Work on this paper was partially supported by NSF CAREER Award 1750780 and CCF Award 2311179.
  • Raichel, Benjamin: Work on this paper was partially supported by NSF CAREER Award 1750780 and CCF Award 2311179.

References

  1. Pankaj K Agarwal, Kyle Fox, Jiangwei Pan, and Rex Ying. Approximating dynamic time warping and edit distance for a pair of point sequences. In Proceedings of the 32nd International Symposium on Computational Geometry, pages 6:1-6:16, 2016. Google Scholar
  2. Mahmuda Ahmed, Sophia Karagiorgou, Dieter Pfoser, and Carola Wenk. Map Construction Algorithms. Springer, 2015. Google Scholar
  3. Helmut Alt and Michael Godau. Computing the Fréchet distance between two polygonal curves. Int. J. Comput. Geometry Appl., 5:75-91, 1995. Google Scholar
  4. Rinat Ben Avraham, Omrit Filtser, Haim Kaplan, Matthew J. Katz, and Micha Sharir. The discrete and semicontinuous Fréchet distance with shortcuts via approximate distance counting and selection. ACM Trans. Algorithms, 11(4):29:1-29:29, 2015. Google Scholar
  5. Karl Bringmann. Why walking the dog takes time: Fréchet distance has no strongly subquadratic algorithms unless SETH fails. In Proceedings of the IEEE 55th Annual Symposium on Foundations of Computer Science, pages 661-670, 2014. Google Scholar
  6. Karl Bringmann and Wolfgang Mulzer. Approximability of the discrete Fréchet distance. JoCG, 7(2):46-76, 2016. Google Scholar
  7. Kevin Buchin, Maarten Löffler, Tim Ophelders, Aleksandr Popov, Jérôme Urhausen, and Kevin Verbeek. Computing the Fréchet distance between uncertain curves in one dimension. Comput. Geom., 109:101923, 2023. URL: https://doi.org/10.1016/j.comgeo.2022.101923.
  8. Maike Buchin, Anne Driemel, and Bettina Speckmann. Computing the Fréchet distance with shortcuts is np-hard. In Siu-Wing Cheng and Olivier Devillers, editors, 30th Annual Symposium on Computational Geometry, page 367. ACM, 2014. URL: https://doi.org/10.1145/2582112.2582144.
  9. Maike Buchin and Lukas Plätz. The k-outlier fréchet distance, 2022. URL: https://arxiv.org/abs/2202.12824.
  10. Daniel Chen, Anne Driemel, Leonidas J. Guibas, Andy Nguyen, and Carola Wenk. Approximate map matching with respect to the Fréchet distance. In Proc. 13th Meeting on Algorithm Engineering and Experiments, pages 75-83, 2011. Google Scholar
  11. Lei Chen and Raymond Ng. On the marriage of Lp-norms and edit distance. In Proceedings of the 30th International Conference on Very Large Databases, pages 792-803, 2004. Google Scholar
  12. Lei Chen, M Tamer Özsu, and Vincent Oria. Robust and fast similarity search for moving object trajectories. In Proceedings of the 2005 ACM SIGMOD International Conference on Management of Data, pages 491-502, 2005. Google Scholar
  13. Jacobus Conradi and Anne Driemel. On Computing the k-Shortcut Fréchet Distance. In Proc. 49th Intern. Colloquium Automata, Languages, Programming, pages 46:1-46:20, 2022. Google Scholar
  14. Anne Driemel and Sariel Har-Peled. Jaywalking your dog: Computing the Fréchet distance with shortcuts. SIAM J. Comput., 42(5):1830-1866, 2013. URL: https://doi.org/10.1137/120865112.
  15. Omrit Filtser and Matthew J. Katz. Algorithms for the discrete Fréchet distance under translation. J. Comput. Geom., 11(1):156-175, 2020. Google Scholar
  16. Kyle Fox and Xinyi Li. Approximating the geometric edit distance. Algorithmica, 84(9):2395-2413, 2022. Google Scholar
  17. Omer Gold and Micha Sharir. Dynamic time warping and geometric edit distance: Breaking the quadratic barrier. ACM Transactions on Algorithms, 14(4):50, 2018. Google Scholar
  18. Leonidas J. Guibas, John Hershberger, Joseph S. B. Mitchell, and Jack Snoeyink. Approximating polygons and subdivisions with minimum link paths. Int. J. Comput. Geom. Appl., 3(4):383-415, 1993. URL: https://doi.org/10.1142/S0218195993000257.
  19. Sariel Har-Peled and Benjamin Raichel. The Fréchet distance revisited and extended. ACM Trans. Algorithms, 10(1):3:1-3:22, 2014. URL: https://doi.org/10.1145/2532646.
  20. Minghui Jiang, Ying Xu, and Binhai Zhu. Protein structure-structure alignment with discrete Fréchet distance. J. Bioinformatics and Computational Biology, 6(1):51-64, 2008. Google Scholar
  21. Pierre-François Marteau. Time warp edit distance with stiffness adjustment for time series matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 31(2):306-318, 2009. Google Scholar
  22. Swaminathan Sankararaman, Pankaj K Agarwal, Thomas Mølhave, Jiangwei Pan, and Arnold P Boedihardjo. Model-driven matching and segmentation of trajectories. In Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 234-243, 2013. Google Scholar
  23. E. Sriraghavendra, Karthik K., and Chiranjib Bhattacharyya. Fréchet distance based approach for searching online handwritten documents. In Proc. 9th Intern. Conf. Document Analysis and Recognition, pages 461-465, 2007. Google Scholar
  24. Aleksandar Stojmirovic and Yi-kuo Yu. Geometric aspects of biological sequence comparison. Journal of Computational Biology, 16(4):579-611, 2009. Google Scholar
  25. Xiaoyue Wang, Abdullah Mueen, Hui Ding, Goce Trajcevski, Peter Scheuermann, and Eamonn Keogh. Experimental comparison of representation methods and distance measures for time series data. Data Mining and Knowledge Discovery, 26(2):275-309, 2013. Google Scholar
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