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A Constant-Factor Approximation for Continuous Dynamic Time Warping in 2D

Authors Kevin Buchin , Maike Buchin , Jan Erik Swiadek , Sampson Wong

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Continuous Dynamic Time Warping
  • Curve Similarity
  • Geometric Approximation Algorithm

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Abstract

Continuous Dynamic Time Warping (CDTW) is a robust similarity measure for polygonal curves that has recently found a variety of applications. Despite its practical use, not much is known about the algorithmic complexity of computing it in 2D, especially when one requires either an exact solution or strong approximation guarantees. We fill this gap by introducing a 5-approximation algorithm with running time O(n⁵) under the 1-norm.
This is the first constant-factor approximation for 2D CDTW with polynomial running time. We extend our algorithm to all polygonal norms on ℝ², which we subsequently use in order to achieve a (5+ε)-approximation with time complexity O(n⁵/ε^{1/2}) for CDTW in 2D under any fixed norm. The latter result in particular includes the usual Euclidean 2-norm.

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Kevin Buchin, Maike Buchin, Jan Erik Swiadek, and Sampson Wong. A Constant-Factor Approximation for Continuous Dynamic Time Warping in 2D. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 47:1-47:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.47

Author Details

Kevin Buchin
  • Technical University Dortmund, Germany
Maike Buchin
  • Ruhr University Bochum, Germany
Jan Erik Swiadek
  • Ruhr University Bochum, Germany
Sampson Wong
  • University of Copenhagen, Denmark

Funding

  • Wong, Sampson: Supported by the European Union’s Marie Skłodowska-Curie Actions Postdoctoral Fellowship, grant no. 101146276.

References

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