License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2022.17
URN: urn:nbn:de:0030-drops-163586
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16358/
Ben-Eliezer, Omri ;
Letzter, Shoham ;
Waingarten, Erik
Finding Monotone Patterns in Sublinear Time, Adaptively
Abstract
We investigate adaptive sublinear algorithms for finding monotone patterns in sequential data. Given fixed 2 ≤ k ∈ m N and ε > 0, consider the problem of finding a length-k increasing subsequence in a sequence f : [n] → ℝ, provided that f is ε-far from free of such subsequences. It was shown by Ben-Eliezer et al. [FOCS 2019] that the non-adaptive query complexity of the above task is Θ((log n)^⌊log₂ k⌋). In this work, we break the non-adaptive lower bound, presenting an adaptive algorithm for this problem which makes O(log n) queries. This is optimal, matching the classical Ω(log n) adaptive lower bound by Fischer [Inf. Comp. 2004] for monotonicity testing (which corresponds to the case k = 2). Equivalently, our result implies that testing whether a sequence decomposes into k monotone subsequences can be done with O(log n) queries.
BibTeX - Entry
@InProceedings{beneliezer_et_al:LIPIcs.ICALP.2022.17,
author = {Ben-Eliezer, Omri and Letzter, Shoham and Waingarten, Erik},
title = {{Finding Monotone Patterns in Sublinear Time, Adaptively}},
booktitle = {49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
pages = {17:1--17:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-235-8},
ISSN = {1868-8969},
year = {2022},
volume = {229},
editor = {Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16358},
URN = {urn:nbn:de:0030-drops-163586},
doi = {10.4230/LIPIcs.ICALP.2022.17},
annote = {Keywords: property testing, monotone patterns, monotone decomposition, adaptivity}
}
Keywords: |
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property testing, monotone patterns, monotone decomposition, adaptivity |
Collection: |
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49th International Colloquium on Automata, Languages, and Programming (ICALP 2022) |
Issue Date: |
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2022 |
Date of publication: |
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28.06.2022 |