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arXiv · 2312.03681

Testing Connectedness of Images

Piotr Berman·Meiram Murzabulatov·Sofya Raskhodnikova·Dragos-Florian Ristache
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Abstract

We investigate algorithms for testing whether an image is connected. Given a proximity parameter $\epsilon\in(0,1)$ and query access to a black-and-white image represented by an $n\times n$ 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 $\epsilon$-far from connected. We show that connectedness can be tested nonadaptively with $O(\frac 1{\epsilon^2})$ queries and adaptively with $O(\frac{1}{\epsilon^{3/2}} \sqrt{\log\frac{1}{\epsilon}})$ queries. The best connectedness tester to date, by Berman, Raskhodnikova, and Yaroslavtsev (STOC 2014) had query complexity $O(\frac 1{\epsilon^2}\log \frac 1{\epsilon})$ and was adaptive. We also prove that every nonadaptive, 1-sided error tester for connectedness must make $\Omega(\frac 1\epsilon\log \frac 1\epsilon)$ queries.

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Piotr Berman, Meiram Murzabulatov, Sofya Raskhodnikova, Dragos-Florian Ristache. 2023-12-06. Testing Connectedness of Images. https://doi.org/10.4230/lipics.approx%2Frandom.2023.66

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