Testing Connectedness of Images

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...

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Bibliographic Details
Published in:Algorithmica Vol. 86; no. 11; pp. 3496 - 3517
Main Authors: Berman, Piotr, Murzabulatov, Meiram, Raskhodnikova, Sofya, Ristache, Dragos-Florian
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2024
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Mathematics of Computing
Queries
Theory of Computation
Computational geometry
Sublinear algorithms
Property testing
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary: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 ϵ 2 ) queries and adaptively with O ( 1 ϵ 3 / 2 log 1 ϵ ) queries. The best connectedness tester to date, by Berman, Raskhodnikova, and Yaroslavtsev (STOC 2014) had query complexity O ( 1 ϵ 2 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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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-024-01248-x