Fundamentals of Computing Continuous Dynamic Time Warping in 2D under Different Norms
Computational Geometry
2026-04-10 v2
Abstract
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 Fr\'echet similarity.
Cite
@article{arxiv.2511.20420,
title = {Fundamentals of Computing Continuous Dynamic Time Warping in 2D under Different Norms},
author = {Kevin Buchin and Maike Buchin and Jan Erik Swiadek and Sampson Wong},
journal= {arXiv preprint arXiv:2511.20420},
year = {2026}
}
Comments
This is the full version of a WALCOM 2026 paper; made minor improvements, mainly in the appendix