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.2023.44
URN: urn:nbn:de:0030-drops-180964
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18096/
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Cohen Sidon, Omer ; Ron, Dana

Sample-Based Distance-Approximation for Subsequence-Freeness

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LIPIcs-ICALP-2023-44.pdf (0.8 MB)

Abstract

In this work, we study the problem of approximating the distance to subsequence-freeness in the sample-based distribution-free model. For a given subsequence (word) w = w_1 … w_k, a sequence (text) T = t_1 … t_n is said to contain w if there exist indices 1 ≤ i_1 < … < i_k ≤ n such that t_{i_{j}} = w_j for every 1 ≤ j ≤ k. Otherwise, T is w-free. Ron and Rosin (ACM TOCT 2022) showed that the number of samples both necessary and sufficient for one-sided error testing of subsequence-freeness in the sample-based distribution-free model is Θ(k/ε).
Denoting by Δ(T,w,p) the distance of T to w-freeness under a distribution p:[n] → [0,1], we are interested in obtaining an estimate Δ̂, such that |Δ̂ - Δ(T,w,p)| ≤ δ with probability at least 2/3, for a given distance parameter δ. Our main result is an algorithm whose sample complexity is Õ(k²/δ²). We first present an algorithm that works when the underlying distribution p is uniform, and then show how it can be modified to work for any (unknown) distribution p. We also show that a quadratic dependence on 1/δ is necessary.

BibTeX - Entry

@InProceedings{cohensidon_et_al:LIPIcs.ICALP.2023.44,
  author =	{Cohen Sidon, Omer and Ron, Dana},
  title =	{{Sample-Based Distance-Approximation for Subsequence-Freeness}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{44:1--44:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18096},
  URN =		{urn:nbn:de:0030-drops-180964},
  doi =		{10.4230/LIPIcs.ICALP.2023.44},
  annote =	{Keywords: Property Testing, Distance Approximation}
}

Keywords: Property Testing, Distance Approximation
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023

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