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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2023.44

Sample-Based Distance-Approximation for Subsequence-Freeness

Authors: Omer Cohen Sidon and Dana Ron

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

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.

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Omer Cohen Sidon and Dana Ron. Sample-Based Distance-Approximation for Subsequence-Freeness. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@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/entities/document/10.4230/LIPIcs.ICALP.2023.44},
  URN =		{urn:nbn:de:0030-drops-180964},
  doi =		{10.4230/LIPIcs.ICALP.2023.44},
  annote =	{Keywords: Property Testing, Distance Approximation}
}

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Sample-Based Distance-Approximation for Subsequence-Freeness

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