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/
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Ben-Eliezer, Omri ; Letzter, Shoham ; Waingarten, Erik

Finding Monotone Patterns in Sublinear Time, Adaptively

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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: property testing, monotone patterns, monotone decomposition, adaptivity
Collection: 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)
Issue Date: 2022
Date of publication: 28.06.2022

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