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Continuous Dynamic Time Warping (CDTW) measures the similarity of polygonal curves robustly to outliers and to sampling rates, but the design and analysis of CDTW algorithms face multiple challenges. We show that CDTW cannot be computed exactly under the Euclidean 2-norm using only algebraic operations, and we give an exact algorithm for CDTW under norms approximating the 2-norm. The latter result relies on technical fundamentals that we establish, and which generalise to any norm and to related measures such as the partial Fréchet similarity.

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Fundamentals of Computing Continuous Dynamic Time Warping in 2D Under Different Norms

  • 会议论文

  • 发表日期：

    2026年

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

摘要

Continuous Dynamic Time Warping (CDTW) measures the similarity of polygonal curves robustly to outliers and to sampling rates, but the design and analysis of CDTW algorithms face multiple challenges. We show that CDTW cannot be computed exactly under the Euclidean 2-norm using only algebraic operations, and we give an exact algorithm for CDTW under norms approximating the 2-norm. The latter result relies on technical fundamentals that we establish, and which generalise to any norm and to related measures such as the partial Fréchet similarity.