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Pattern matching under DTW distance

Abstract

In this work, we consider the problem of pattern matching under the dynamic time warping (DTW) distance motivated by potential applications in the analysis of biological data produced by the third generation sequencing. To measure the DTW distance between two strings, one must "warp" them, that is, double some letters in the strings to obtain two equal-lengths strings, and then sum the distances between the letters in the corresponding positions. When the distances between letters are integers, we show that for a pattern P with m runs and a text T with n runs: 1. There is an O(m + n)-time algorithm that computes all locations where the DTW distance from P to T is at most 1; 2. There is an O(kmn)-time algorithm that computes all locations where the DTW distance from P to T is at most k. As a corollary of the second result, we also derive an approximation algorithm for general metrics on the alphabet.
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Dates and versions

hal-03763091 , version 1 (30-08-2022)

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Garance Gourdel, Anne Driemel, Pierre Peterlongo, Tatiana Starikovskaya. Pattern matching under DTW distance. SPIRE 2022 - 29th International Symposium on String Processing and Information Retrieval, Nov 2022, Concepción, Chile. pp.315--330. ⟨hal-03763091⟩
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