research-article

Dynamic Time Warping and Geometric Edit Distance: Breaking the Quadratic Barrier

Authors:

Micha SharirAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 14, Issue 4

Article No.: 50, Pages 1 - 17

https://doi.org/10.1145/3230734

Published: 21 August 2018 Publication History

Abstract

Dynamic Time Warping (DTW) and Geometric Edit Distance (GED) are basic similarity measures between curves or general temporal sequences (e.g., time series) that are represented as sequences of points in some metric space (X, dist). The DTW and GED measures are massively used in various fields of computer science and computational biology. Consequently, the tasks of computing these measures are among the core problems in P. Despite extensive efforts to find more efficient algorithms, the best-known algorithms for computing the DTW or GED between two sequences of points in X = R^d are long-standing dynamic programming algorithms that require quadratic runtime, even for the one-dimensional case d = 1, which is perhaps one of the most used in practice.

In this article, we break the nearly 50-year-old quadratic time bound for computing DTW or GED between two sequences of n points in R by presenting deterministic algorithms that run in O(n² log log log n/ log log n) time. Our algorithms can be extended to work also for higher-dimensional spaces R^d, for any constant d, when the underlying distance-metric dist is polyhedral (e.g., L₁, L_infin).

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Index Terms

Dynamic Time Warping and Geometric Edit Distance: Breaking the Quadratic Barrier
1. Theory of computation
  1. Design and analysis of algorithms
  2. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 14, Issue 4

October 2018

445 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3266298

Editor:
Aravind Srinivasan
University of Maryland, USA

Issue’s Table of Contents

Copyright © 2018 ACM.

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Publication History

Published: 21 August 2018

Accepted: 01 June 2018

Revised: 01 April 2018

Received: 01 October 2017

Published in TALG Volume 14, Issue 4

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U.S.-Israeli Binational Science Foundation (BSF)
Hermann Minkowski-MINERVA Center for Geometry at Tel Aviv University
Israel Science Foundation (ISF)
Israeli Centers of Research Excellence (I-CORE) program
Blavatnik Research Fund in Computer Science at Tel Aviv University

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https://doi.org/10.1109/CVPRW63382.2024.00261
Li YZhou LLi ZChe TLee PLu YHu Y(2024)Dynamic behaviour and energy dissipation of offline air pockets in transient pipe flowsEngineering Applications of Computational Fluid Mechanics10.1080/19942060.2024.238706018:1Online publication date: 7-Aug-2024
https://doi.org/10.1080/19942060.2024.2387060
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