Õptimal Dynamic Time Warping on Run-Length Encoded Strings

Itai Boneh; Shay Golan; Shay Mozes; Oren Weimann

doi:10.4230/LIPIcs.ICALP.2024.30

Õptimal Dynamic Time Warping on Run-Length Encoded Strings

Itai Boneh, Shay Golan, Shay Mozes, Oren Weimann

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Dynamic Time Warping (DTW) distance is the optimal cost of matching two strings when extending runs of letters is for free. Therefore, it is natural to measure the time complexity of DTW in terms of the number of runs n (rather than the string lengths N). In this paper, we give an Õ(n²) time algorithm for computing the DTW distance. This matches (up to log factors) the known (conditional) lower bound, and should be compared with the previous fastest O(n³) time exact algorithm and the Õ(n²) time approximation algorithm. Our method also immediately implies an Õ(nk) time algorithm when the distance is bounded by k. This should be compared with the previous fastest O(n²k) and O(Nk) time exact algorithms and the Õ(nk) time approximation algorithm.

Original language	English
Title of host publication	51st International Colloquium on Automata, Languages, and Programming, ICALP 2024
Editors	Karl Bringmann, Martin Grohe, Gabriele Puppis, Ola Svensson
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959773225
DOIs	https://doi.org/10.4230/LIPIcs.ICALP.2024.30
State	Published - Jul 2024
Externally published	Yes
Event	51st International Colloquium on Automata, Languages, and Programming, ICALP 2024 - Tallinn, Estonia Duration: 8 Jul 2024 → 12 Jul 2024

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	297
ISSN (Print)	1868-8969

Conference

Conference	51st International Colloquium on Automata, Languages, and Programming, ICALP 2024
Country/Territory	Estonia
City	Tallinn
Period	8/07/24 → 12/07/24

Bibliographical note

Publisher Copyright:
© Itai Boneh, Shay Golan, Shay Mozes, and Oren Weimann.

Keywords

Dynamic time warping
edit distance
Fréchet distance
run-length encoding

Access to Document

10.4230/LIPIcs.ICALP.2024.30

Cite this

Boneh, I., Golan, S., Mozes, S., & Weimann, O. (2024). Õptimal Dynamic Time Warping on Run-Length Encoded Strings. In K. Bringmann, M. Grohe, G. Puppis, & O. Svensson (Eds.), 51st International Colloquium on Automata, Languages, and Programming, ICALP 2024 Article 30 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 297). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ICALP.2024.30

Boneh, Itai ; Golan, Shay ; Mozes, Shay et al. / Õptimal Dynamic Time Warping on Run-Length Encoded Strings. 51st International Colloquium on Automata, Languages, and Programming, ICALP 2024. editor / Karl Bringmann ; Martin Grohe ; Gabriele Puppis ; Ola Svensson. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2024. (Leibniz International Proceedings in Informatics, LIPIcs).

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abstract = "Dynamic Time Warping (DTW) distance is the optimal cost of matching two strings when extending runs of letters is for free. Therefore, it is natural to measure the time complexity of DTW in terms of the number of runs n (rather than the string lengths N). In this paper, we give an {\~O}(n2) time algorithm for computing the DTW distance. This matches (up to log factors) the known (conditional) lower bound, and should be compared with the previous fastest O(n3) time exact algorithm and the {\~O}(n2) time approximation algorithm. Our method also immediately implies an {\~O}(nk) time algorithm when the distance is bounded by k. This should be compared with the previous fastest O(n2k) and O(Nk) time exact algorithms and the {\~O}(nk) time approximation algorithm.",

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author = "Itai Boneh and Shay Golan and Shay Mozes and Oren Weimann",

note = "Publisher Copyright: {\textcopyright} Itai Boneh, Shay Golan, Shay Mozes, and Oren Weimann.; 51st International Colloquium on Automata, Languages, and Programming, ICALP 2024 ; Conference date: 08-07-2024 Through 12-07-2024",

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Boneh, I, Golan, S, Mozes, S & Weimann, O 2024, Õptimal Dynamic Time Warping on Run-Length Encoded Strings. in K Bringmann, M Grohe, G Puppis & O Svensson (eds), 51st International Colloquium on Automata, Languages, and Programming, ICALP 2024., 30, Leibniz International Proceedings in Informatics, LIPIcs, vol. 297, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 51st International Colloquium on Automata, Languages, and Programming, ICALP 2024, Tallinn, Estonia, 8/07/24. https://doi.org/10.4230/LIPIcs.ICALP.2024.30

Õptimal Dynamic Time Warping on Run-Length Encoded Strings. / Boneh, Itai; Golan, Shay; Mozes, Shay et al.
51st International Colloquium on Automata, Languages, and Programming, ICALP 2024. ed. / Karl Bringmann; Martin Grohe; Gabriele Puppis; Ola Svensson. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2024. 30 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 297).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Õptimal Dynamic Time Warping on Run-Length Encoded Strings

AU - Boneh, Itai

AU - Golan, Shay

AU - Mozes, Shay

AU - Weimann, Oren

N1 - Publisher Copyright: © Itai Boneh, Shay Golan, Shay Mozes, and Oren Weimann.

PY - 2024/7

Y1 - 2024/7

N2 - Dynamic Time Warping (DTW) distance is the optimal cost of matching two strings when extending runs of letters is for free. Therefore, it is natural to measure the time complexity of DTW in terms of the number of runs n (rather than the string lengths N). In this paper, we give an Õ(n2) time algorithm for computing the DTW distance. This matches (up to log factors) the known (conditional) lower bound, and should be compared with the previous fastest O(n3) time exact algorithm and the Õ(n2) time approximation algorithm. Our method also immediately implies an Õ(nk) time algorithm when the distance is bounded by k. This should be compared with the previous fastest O(n2k) and O(Nk) time exact algorithms and the Õ(nk) time approximation algorithm.

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KW - Fréchet distance

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Boneh I, Golan S, Mozes S, Weimann O. Õptimal Dynamic Time Warping on Run-Length Encoded Strings. In Bringmann K, Grohe M, Puppis G, Svensson O, editors, 51st International Colloquium on Automata, Languages, and Programming, ICALP 2024. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2024. 30. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.ICALP.2024.30

Õptimal Dynamic Time Warping on Run-Length Encoded Strings

Abstract

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Bibliographical note

Keywords

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