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DOI: 10.4230/LIPIcs.SoCG.2016.6
Approximating Dynamic Time Warping and Edit Distance for a Pair of Point Sequences

Authors: Pankaj K. Agarwal, Kyle Fox, Jiangwei Pan, and Rex Ying

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract
We present the first subquadratic algorithms for computing similarity between a pair of point sequences in R^d, for any fixed d > 1, using dynamic time warping (DTW) and edit distance, assuming that the point sequences are drawn from certain natural families of curves. In particular, our algorithms compute (1 + eps)-approximations of DTW and ED in near-linear time for point sequences drawn from k-packed or k-bounded curves, and subquadratic time for backbone sequences. Roughly speaking, a curve is k-packed if the length of its intersection with any ball of radius r is at most kr, and it is k-bounded if the sub-curve between two curve points does not go too far from the two points compared to the distance between the two points. In backbone sequences, consecutive points are spaced at approximately equal distances apart, and no two points lie very close together. Recent results suggest that a subquadratic algorithm for DTW or ED is unlikely for an arbitrary pair of point sequences even for d = 1. The commonly used dynamic programming algorithms for these distance measures reduce the problem to computing a minimum-weight path in a grid graph. Our algorithms work by constructing a small set of rectangular regions that cover the grid vertices. The weights of vertices inside each rectangle are roughly the same, and we develop efficient procedures to compute the approximate minimum-weight paths through these rectangles.
Cite as

Pankaj K. Agarwal, Kyle Fox, Jiangwei Pan, and Rex Ying. Approximating Dynamic Time Warping and Edit Distance for a Pair of Point Sequences. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{agarwal_et_al:LIPIcs.SoCG.2016.6,
  author =	{Agarwal, Pankaj K. and Fox, Kyle and Pan, Jiangwei and Ying, Rex},
  title =	{{Approximating Dynamic Time Warping and Edit Distance for a Pair of Point Sequences}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.6},
  URN =		{urn:nbn:de:0030-drops-58989},
  doi =		{10.4230/LIPIcs.SoCG.2016.6},
  annote =	{Keywords: Dynamic time warping, Edit distance, Near-linear-time algorithm, Dynamic programming, Well-separated pair decomposition}
}
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