License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2019.16
URN: urn:nbn:de:0030-drops-104203
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10420/
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Braverman, Vladimir ; Charikar, Moses ; Kuszmaul, William ; Woodruff, David P. ; Yang, Lin F.

The One-Way Communication Complexity of Dynamic Time Warping Distance

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LIPIcs-SoCG-2019-16.pdf (0.5 MB)

Abstract

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).

BibTeX - Entry

@InProceedings{braverman_et_al:LIPIcs:2019:10420,
  author =	{Vladimir Braverman and Moses Charikar and William Kuszmaul and David P. Woodruff and Lin F. Yang},
  title =	{{The One-Way Communication Complexity of Dynamic Time Warping Distance}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10420},
  URN =		{urn:nbn:de:0030-drops-104203},
  doi =		{10.4230/LIPIcs.SoCG.2019.16},
  annote =	{Keywords: dynamic time warping, one-way communication complexity, tree metrics}
}

Keywords: dynamic time warping, one-way communication complexity, tree metrics
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019

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