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Approximating the Fréchet Distance When Only One Curve Is c-Packed

Authors Joachim Gudmundsson , Tiancheng Mai , Sampson Wong

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Author Details

Joachim Gudmundsson
  • School of Computer Science, University of Sydney, Australia
Tiancheng Mai
  • School of Computer Science, University of Sydney, Australia
Sampson Wong
  • Department of Computer Science, University of Copenhagen, Denmark

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Joachim Gudmundsson, Tiancheng Mai, and Sampson Wong. Approximating the Fréchet Distance When Only One Curve Is c-Packed. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 37:1-37:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ISAAC.2024.37

Abstract

One approach to studying the Fréchet distance is to consider curves that satisfy realistic assumptions. By now, the most popular realistic assumption for curves is c-packedness. Existing algorithms for computing the Fréchet distance between c-packed curves require both curves to be c-packed. In this paper, we only require one of the two curves to be c-packed. Our result is a nearly-linear time algorithm that (1+ε)-approximates the Fréchet distance between a c-packed curve and a general curve in ℝ^d, for constant values of ε, d and c.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Fréchet distance
  • c-packed curve
  • approximation algorithm

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