Binary Dynamic Time Warping in Linear Time
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Dynamic time warping distance (DTW) is a widely used distance measure between time series x, y ∈Σ^n. It was shown by Abboud, Backurs, and Williams that in the binary case, where |Σ| = 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 Õ(k + ℓ), where k and ℓ are the number of runs in x and y, respectively. This improves on the previous best bound of O(kℓ) due to Dupont and Marteau.
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