License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2022.90
URN: urn:nbn:de:0030-drops-170281
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17028/
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Xi, Zoe ; Kuszmaul, William

Approximating Dynamic Time Warping Distance Between Run-Length Encoded Strings

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LIPIcs-ESA-2022-90.pdf (0.7 MB)

Abstract

Dynamic Time Warping (DTW) is a widely used similarity measure for comparing strings that encode time series data, with applications to areas including bioinformatics, signature verification, and speech recognition. The standard dynamic-programming algorithm for DTW takes O(n²) time, and there are conditional lower bounds showing that no algorithm can do substantially better.
In many applications, however, the strings x and y may contain long runs of repeated letters, meaning that they can be compressed using run-length encoding. A natural question is whether the DTW-distance between these compressed strings can be computed efficiently in terms of the lengths k and ? of the compressed strings. Recent work has shown how to achieve O(k?² + ? k²) time, leaving open the question of whether a near-quadratic Õ(k?)-time algorithm might exist.
We show that, if a small approximation loss is permitted, then a near-quadratic time algorithm is indeed possible: our algorithm computes a (1 + ε)-approximation for DTW(x, y) in Õ(k? / ε³) time, where k and ? are the number of runs in x and y. Our algorithm allows for DTW to be computed over any metric space (Σ, δ) in which distances are O(log n)-bit integers. Surprisingly, the algorithm also works even if δ does not induce a metric space on Σ (e.g., δ need not satisfy the triangle inequality).

BibTeX - Entry

@InProceedings{xi_et_al:LIPIcs.ESA.2022.90,
  author =	{Xi, Zoe and Kuszmaul, William},
  title =	{{Approximating Dynamic Time Warping Distance Between Run-Length Encoded Strings}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{90:1--90:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17028},
  URN =		{urn:nbn:de:0030-drops-170281},
  doi =		{10.4230/LIPIcs.ESA.2022.90},
  annote =	{Keywords: Dynamic time warping distance, approximation algorithms, run-length encodings, computational geometry}
}

Keywords: Dynamic time warping distance, approximation algorithms, run-length encodings, computational geometry
Collection: 30th Annual European Symposium on Algorithms (ESA 2022)
Issue Date: 2022
Date of publication: 01.09.2022

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