Gold, Omer ;
Sharir, Micha
Dynamic Time Warping and Geometric Edit Distance: Breaking the Quadratic Barrier
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 bestknown algorithms for computing the DTW or GED between two sequences of points in X = R^d are longstanding dynamic programming algorithms that require quadratic runtime, even for the onedimensional case d = 1, which is perhaps one of the most used in practice.
In this paper, we break the nearly 50 years 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( n^2 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 distancemetric dist is polyhedral (e.g., L_1, L_infty).
BibTeX  Entry
@InProceedings{gold_et_al:LIPIcs:2017:7382,
author = {Omer Gold and Micha Sharir},
title = {{Dynamic Time Warping and Geometric Edit Distance: Breaking the Quadratic Barrier}},
booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
pages = {25:125:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770415},
ISSN = {18688969},
year = {2017},
volume = {80},
editor = {Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7382},
URN = {urn:nbn:de:0030drops73820},
doi = {10.4230/LIPIcs.ICALP.2017.25},
annote = {Keywords: Dynamic Time Warping, Geometric Edit Distance, Time Series, Points Matching, Geometric Matching}
}
2017
Keywords: 

Dynamic Time Warping, Geometric Edit Distance, Time Series, Points Matching, Geometric Matching 
Seminar: 

44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Issue date: 

2017 
Date of publication: 

2017 