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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.

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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.

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