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Testing Connectedness of Images

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

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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.

Cite AsGet BibTex

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

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.

Subject Classification

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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