Document Open Access Logo

Testing Connectedness of Images

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

PDF
Thumbnail PDF

File

LIPIcs.APPROX-RANDOM.2023.66.pdf
  • Filesize: 0.9 MB
  • 15 pages

Document Identifiers

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 As Get 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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Noga Alon, Omri Ben-Eliezer, and Eldar Fischer. Testing hereditary properties of ordered graphs and matrices. In Chris Umans, editor, 58th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2017, Berkeley, CA, USA, October 15-17, 2017, pages 848-858. IEEE Computer Society, 2017. URL: https://doi.org/10.1109/FOCS.2017.83.
  2. Omri Ben-Eliezer and Eldar Fischer. Earthmover resilience and testing in ordered structures. In Rocco A. Servedio, editor, 33rd Computational Complexity Conference, CCC 2018, June 22-24, 2018, San Diego, CA, USA, volume 102 of LIPIcs, pages 18:1-18:35. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.CCC.2018.18.
  3. Omri Ben-Eliezer, Simon Korman, and Daniel Reichman. Deleting and testing forbidden patterns in multi-dimensional arrays. In Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl, editors, 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10-14, 2017, Warsaw, Poland, volume 80 of LIPIcs, pages 9:1-9:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.ICALP.2017.9.
  4. Petra Berenbrink, Bruce Krayenhoff, and Frederik Mallmann-Trenn. Estimating the number of connected components in sublinear time. Inf. Process. Lett., 114(11):639-642, 2014. URL: https://doi.org/10.1016/j.ipl.2014.05.008.
  5. Piotr Berman, Meiram Murzabulatov, and Sofya Raskhodnikova. The power and limitations of uniform samples in testing properties of figures. Algorithmica, 81(3):1247-1266, 2019. Google Scholar
  6. Piotr Berman, Meiram Murzabulatov, and Sofya Raskhodnikova. Testing figures under the uniform distribution. Random Struct. Algorithms, 54(3):413-443, 2019. Google Scholar
  7. Piotr Berman, Meiram Murzabulatov, and Sofya Raskhodnikova. Tolerant testers of image properties. ACM Transactions on Algorithms (TALG), 18(4):1-39, 2022. Google Scholar
  8. Piotr Berman, Sofya Raskhodnikova, and Grigory Yaroslavtsev. L_p-testing. In David B. Shmoys, editor, Symposium on Theory of Computing, STOC 2014, New York, NY, USA, May 31 - June 03, 2014, pages 164-173. ACM, 2014. URL: https://doi.org/10.1145/2591796.2591887.
  9. Bernard Chazelle, Ronitt Rubinfeld, and Luca Trevisan. Approximating the minimum spanning tree weight in sublinear time. SIAM J. Comput., pages 1370-1379, 2005. URL: https://doi.org/10.1137/S0097539702403244.
  10. Eldar Fischer and Ilan Newman. Testing of matrix-poset properties. Comb., 27(3):293-327, 2007. URL: https://doi.org/10.1007/s00493-007-2154-3.
  11. Oded Goldreich, Shafi Goldwasser, and Dana Ron. Property testing and its connection to learning and approximation. J. ACM, 45(4):653-750, 1998. URL: https://doi.org/10.1145/285055.285060.
  12. Oded Goldreich and Dana Ron. Property testing in bounded degree graphs. Algorithmica, 32(2):302-343, 2002. URL: https://doi.org/10.1007/s00453-001-0078-7.
  13. Igor Kleiner, Daniel Keren, Ilan Newman, and Oren Ben-Zwi. Applying property testing to an image partitioning problem. IEEE Trans. Pattern Anal. Mach. Intell., 33(2):256-265, 2011. URL: https://doi.org/10.1109/TPAMI.2010.165.
  14. Simon Korman, Daniel Reichman, and Gilad Tsur. Tight approximation of image matching. CoRR, abs/1111.1713, 2011. URL: https://arxiv.org/abs/1111.1713.
  15. Simon Korman, Daniel Reichman, Gilad Tsur, and Shai Avidan. Fast-match: Fast affine template matching. In CVPR, pages 2331-2338. IEEE, 2013. URL: https://doi.org/10.1109/CVPR.2013.302.
  16. Marvin Minsky and Seymour A. Papert. Perceptrons: An Introduction to Computational Geometry. The MIT Press, September 2017. URL: https://doi.org/10.7551/mitpress/11301.001.0001.
  17. Pritam Paral, Amitava Chatterjee, and Anjan Rakshit. Vision sensor-based shoe detection for human tracking in a human-robot coexisting environment: A photometric invariant approach using dbscan algorithm. IEEE Sensors Journal, 19(12):4549-4559, 2019. Google Scholar
  18. Sofya Raskhodnikova. Approximate testing of visual properties. In Sanjeev Arora, Klaus Jansen, José D. P. Rolim, and Amit Sahai, editors, RANDOM-APPROX, volume 2764 of Lecture Notes in Computer Science, pages 370-381. Springer, 2003. URL: https://doi.org/10.1007/978-3-540-45198-3_31.
  19. Dana Ron and Gilad Tsur. Testing properties of sparse images. ACM Trans. Algorithms, 10(4):17:1-17:52, 2014. URL: https://doi.org/10.1145/2635806.
  20. Ronitt Rubinfeld and Madhu Sudan. Robust characterizations of polynomials with applications to program testing. SIAM J. Comput., 25(2):252-271, 1996. Google Scholar
  21. Andrew C. Yao. Probabilistic computation, towards a unified measure of complexity. In Proceedings of the Eighteenth Annual Symposium on Foundations of Computer Science, pages 222-227, 1977. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact