The One-Way Communication Complexity of Dynamic Time Warping Distance

Authors Vladimir Braverman, Moses Charikar, William Kuszmaul, David P. Woodruff, Lin F. Yang

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Author Details

Vladimir Braverman
  • Johns Hopkins University, Baltimore MD, USA
Moses Charikar
  • Stanford University, Stanford CA, USA
William Kuszmaul
  • Massachusetts Institute of Technology, Cambridge MA, USA
David P. Woodruff
  • Carnegie Mellon University, Pittsburgh PA, USA
Lin F. Yang
  • Princeton University, Princeton NJ, USA


David P. Woodruff would like to thank the Simons Institute for the Theory of Computing where part of this work was done.

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Vladimir Braverman, Moses Charikar, William Kuszmaul, David P. Woodruff, and Lin F. Yang. The One-Way Communication Complexity of Dynamic Time Warping Distance. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We resolve the randomized one-way communication complexity of Dynamic Time Warping (DTW) distance. We show that there is an efficient one-way communication protocol using O~(n/alpha) bits for the problem of computing an alpha-approximation for DTW between strings x and y of length n, and we prove a lower bound of Omega(n / alpha) bits for the same problem. Our communication protocol works for strings over an arbitrary metric of polynomial size and aspect ratio, and we optimize the logarithmic factors depending on properties of the underlying metric, such as when the points are low-dimensional integer vectors equipped with various metrics or have bounded doubling dimension. We also consider linear sketches of DTW, showing that such sketches must have size Omega(n).

Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
  • dynamic time warping
  • one-way communication complexity
  • tree metrics


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