A reduction of the dynamic time warping distance to the longest increasing subsequence length

Yoshifumi Sakai, Shunsuke Inenaga

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The similarity between a pair of time series, i.e., sequences of indexed values in time order, is often estimated by the dynamic time warping (DTW) distance, instead of any in the well-studied family of measures including the longest common subsequence (LCS) length and the edit distance. Although it may seem as if the DTW and the LCS(-like) measures are essentially different, we reveal that the DTW distance can be represented by the longest increasing subsequence (LIS) length of a sequence of integers, which is the LCS length between the integer sequence and itself sorted. For a given pair of time series of n integers between zero and c, we propose an integer sequence that represents any substring-substring DTW distance as its band-substring LIS length. The length of the produced integer sequence is O(c4n2) or O(c2n2) depending on the variant of the DTW distance used, both of which can be translated to O(n2) for constant cost functions. To demonstrate that techniques developed under the LCS(-like) measures are directly applicable to analysis of time series via our reduction of DTW to LIS, we present time-efficient algorithms for DTW-related problems utilizing the semi-local sequence comparison technique developed for LCS-related problems.

Original languageEnglish
Title of host publication31st International Symposium on Algorithms and Computation, ISAAC 2020
EditorsYixin Cao, Siu-Wing Cheng, Minming Li
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages61-616
Number of pages556
ISBN (Electronic)9783959771733
DOIs
Publication statusPublished - Dec 2020
Event31st International Symposium on Algorithms and Computation, ISAAC 2020 - Virtual, Hong Kong, China
Duration: Dec 14 2020Dec 18 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume181
ISSN (Print)1868-8969

Conference

Conference31st International Symposium on Algorithms and Computation, ISAAC 2020
CountryChina
CityVirtual, Hong Kong
Period12/14/2012/18/20

All Science Journal Classification (ASJC) codes

  • Software

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