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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2023.54
URN: urn:nbn:de:0030-drops-185889
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18588/
Holznigenkemper, Jana ;
Komusiewicz, Christian ;
Morawietz, Nils ;
Seeger, Bernhard
On the Complexity of Computing Time Series Medians Under the Move-Split-Merge Metric
Abstract
We initiate a study of the complexity of MSM-Median, the problem of computing a median of a set of k real-valued time series under the move-split-merge distance. This distance measure is based on three operations: moves, which may shift a data point in a time series; splits, which replace one data point in a time series by two consecutive data points of the same value; and merges, which replace two consecutive data points of equal value by a single data point of the same value. The cost of a move operation is the difference of the data point value before and after the operation, the cost of split and merge operations is defined via a given constant c.
Our main results are as follows. First, we show that MSM-Median is NP-hard and W[1]-hard with respect to k for time series with at most three distinct values. Under the Exponential Time Hypothesis (ETH) our reduction implies that a previous dynamic programming algorithm with running time |I|^?(k) [Holznigenkemper et al., Data Min. Knowl. Discov. '23] is essentially optimal. Here, |I| denotes the total input size. Second, we show that MSM-Median can be solved in 2^?(d/c)⋅|I|^?(1) time where d is the total distance of the median to the input time series.
BibTeX - Entry
@InProceedings{holznigenkemper_et_al:LIPIcs.MFCS.2023.54,
author = {Holznigenkemper, Jana and Komusiewicz, Christian and Morawietz, Nils and Seeger, Bernhard},
title = {{On the Complexity of Computing Time Series Medians Under the Move-Split-Merge Metric}},
booktitle = {48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
pages = {54:1--54:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-292-1},
ISSN = {1868-8969},
year = {2023},
volume = {272},
editor = {Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/18588},
URN = {urn:nbn:de:0030-drops-185889},
doi = {10.4230/LIPIcs.MFCS.2023.54},
annote = {Keywords: Parameterized Complexity, Median String, Time Series, ETH}
}
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Keywords: |
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Parameterized Complexity, Median String, Time Series, ETH |
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Collection: |
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48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023) |
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Issue Date: |
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2023 |
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Date of publication: |
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21.08.2023 |
