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Testing Connectedness of Images

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

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ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Property testing
  • sublinear-algorithms
  • lower bounds
  • connectivity
  • graphs

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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) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.66

Author Details

Piotr Berman
  • Unaffiliated Researcher
Meiram Murzabulatov
  • Computer Science Department, School of Digital Sciences, Nazarbayev University, Astana, Kazakhstan
Sofya Raskhodnikova
  • Boston University, MA, USA
Dragos Ristache
  • Boston University, MA, USA

Funding

  • Murzabulatov, Meiram: Supported by the Nazarbayev University Social Policy Grant.

References

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