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DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.66

Testing Connectedness of Images

Authors: Piotr Berman, Meiram Murzabulatov, Sofya Raskhodnikova, and Dragos Ristache

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract

We investigate algorithms for testing whether an image is connected. Given a proximity parameter ε ∈ (0,1) and query access to a black-and-white image represented by an n×n matrix of Boolean pixel values, a (1-sided error) connectedness tester accepts if the image is connected and rejects with probability at least 2/3 if the image is ε-far from connected. We show that connectedness can be tested nonadaptively with O(1/ε²) queries and adaptively with O(1/ε^{3/2} √{log1/ε}) queries. The best connectedness tester to date, by Berman, Raskhodnikova, and Yaroslavtsev (STOC 2014) had query complexity O(1/ε² log 1/ε) and was adaptive. We also prove that every nonadaptive, 1-sided error tester for connectedness must make Ω(1/ε log 1/ε) queries.

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Piotr Berman, Meiram Murzabulatov, Sofya Raskhodnikova, and Dragos Ristache. Testing Connectedness of Images. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 66:1-66:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{berman_et_al:LIPIcs.APPROX/RANDOM.2023.66,
  author =	{Berman, Piotr and Murzabulatov, Meiram and Raskhodnikova, Sofya and Ristache, Dragos},
  title =	{{Testing Connectedness of Images}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{66:1--66:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.66},
  URN =		{urn:nbn:de:0030-drops-188918},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.66},
  annote =	{Keywords: Property testing, sublinear-algorithms, lower bounds, connectivity, graphs}
}

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Testing Connectedness of Images

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