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arXiv · 2101.01108

Binary Dynamic Time Warping in Linear Time

William Kuszmaul
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Abstract

Dynamic time warping distance (DTW) is a widely used distance measure between time series $x, y \in \Sigma^n$. It was shown by Abboud, Backurs, and Williams that in the \emph{binary case}, where $|\Sigma| = 2$, DTW can be computed in time $O(n^{1.87})$. We improve this running time $O(n)$. Moreover, if $x$ and $y$ are run-length encoded, then there is an algorithm running in time $\tilde{O}(k + \ell)$, where $k$ and $\ell$ are the number of runs in $x$ and $y$, respectively. This improves on the previous best bound of $O(k\ell)$ due to Dupont and Marteau.

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William Kuszmaul. 2021-01-04. Binary Dynamic Time Warping in Linear Time. https://arxiv.org/abs/2101.01108

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