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.

翻译：连续动态时间规整（CDTW）能够鲁棒地度量多边形曲线的相似性，不受离群值和采样率的影响，但CDTW算法的设计与分析面临多重挑战。我们证明，在欧几里得2-范数下，仅通过代数运算无法精确计算CDTW，并给出了一种在近似2-范数的范数下精确计算CDTW的算法。后一结论依赖于我们建立的技术基础，这些基础可推广至任意范数及部分弗雷歇相似度等相关度量。