Document Open Access Logo

A Two-Sided Error Distributed Property Tester For Conductance

Authors Hendrik Fichtenberger , Yadu Vasudev

PDF
Thumbnail PDF

File

LIPIcs.MFCS.2018.19.pdf
  • Filesize: 488 kB
  • 15 pages

Document Identifiers

Author Details

Hendrik Fichtenberger
  • TU Dortmund, Dortmund, Germany
Yadu Vasudev
  • Indian Institute of Technology Madras, Chennai, India

Funding

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ ERC grant agreement no 307696.

Cite AsGet BibTex

Hendrik Fichtenberger and Yadu Vasudev. A Two-Sided Error Distributed Property Tester For Conductance. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 19:1-19:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.MFCS.2018.19

Abstract

We study property testing in the distributed model and extend its setting from testing with one-sided error to testing with two-sided error. In particular, we develop a two-sided error property tester for general graphs with round complexity O(log(n) / (epsilon Phi^2)) in the CONGEST model, which accepts graphs with conductance Phi and rejects graphs that are epsilon-far from having conductance at least Phi^2 / 1000 with constant probability. Our main insight is that one can start poly(n) random walks from a few random vertices without violating the congestion and unite the results to obtain a consistent answer from all vertices. For connected graphs, this is even possible when the number of vertices is unknown. We also obtain a matching Omega(log n) lower bound for the LOCAL and CONGEST models by an indistinguishability argument. Although the power of vertex labels that arises from two-sided error might seem to be much stronger than in the sequential query model, we can show that this is not the case.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • property testing
  • distributed algorithms
  • conductance

Metrics

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

Related Versions

References

  1. Zvika Brakerski and Boaz Patt-Shamir. Distributed discovery of large near-cliques. Distributed Computing, 24(2), 2011. URL: http://dx.doi.org/10.1007/s00446-011-0132-x.
  2. Keren Censor-Hillel, Eldar Fischer, Gregory Schwartzman, and Yadu Vasudev. Fast distributed algorithms for testing graph properties. In Proceedings of the 30th International Symposium on Distributed Computing (DISC), 2016. Google Scholar
  3. Fan R. K. Chung. Diameters and eigenvalues. Journal of the American Mathematical Society, 2(2), 1989. Google Scholar
  4. Fan R. K. Chung. Spectral Graph Theory. American Mathematical Society, 1997. Google Scholar
  5. Artur Czumaj, Pan Peng, and Christian Sohler. Testing cluster structure of graphs. In Proccedings of the 47th ACM Symposium on Theory of Computing (STOC), 2015. Google Scholar
  6. Artur Czumaj and Christian Sohler. Testing expansion in bounded-degree graphs. In Proccedings of the 48th IEEE Symposium on Foundations of Computer Science (FOCS), 2007. Google Scholar
  7. Atish Das Sarma, Danupon Nanongkai, Gopal Pandurangan, and Prasad Tetali. Distributed random walks. Journal of the ACM (JACM), 60(1), 2013. Google Scholar
  8. Guy Even, Orr Fischer, Pierre Fraigniaud, Tzlil Gonen, Reut Levi, Moti Medina, Pedro Montealegre, Dennis Olivetti, Rotem Oshman, Ivan Rapaport, and Ioan Todinca. Three Notes on Distributed Property Testing. In Proceedings of the 31st International Symposium on Distributed Computing (DISC), 2017. Google Scholar
  9. Hendrik Fichtenberger, Pan Peng, and Christian Sohler. On constant-size graphs that preserve the local structure of high-girth graphs. In Proccedings of the 19th International Workshop on Randomization and Computation (RANDOM), 2015. Google Scholar
  10. Hendrik Fichtenberger and Yadu Vasudev. A Two-Sided Error Distributed Property Tester For Conductance. arXiv:1705.08174, 2018. URL: http://arxiv.org/abs/1705.08174.
  11. Pierre Fraigniaud, Ivan Rapaport, Ville Salo, and Ioan Todinca. Distributed testing of excluded subgraphs. In Proceedings of the 30th International Symposium on Distributed Computing (DISC), 2016. Google Scholar
  12. Oded Goldreich. Introduction to testing graph properties. In Property Testing. Springer, 2010. Google Scholar
  13. Oded Goldreich. Introduction to Property Testing. Cambridge University Press, 2017. Google Scholar
  14. Oded Goldreich, Shari Goldwasser, and Dana Ron. Property Testing and Its Connection to Learning and Approximation. Journal of the ACM (JACM), 45(4), 1998. URL: http://dx.doi.org/10.1145/285055.285060.
  15. Oded Goldreich and Dana Ron. On Testing Expansion in Bounded-Degree Graphs. Electronic Colloquium on Computational Complexity (ECCC), 2000. URL: https://eccc.weizmann.ac.il/report/2000/020/.
  16. Satyen Kale and C. Seshadhri. An expansion tester for bounded degree graphs. SIAM Journal on Computing (SICOMP), 40(3), 2011. URL: http://dx.doi.org/10.1137/100802980.
  17. Angsheng Li, Yicheng Pan, and Pan Peng. Testing Conductance in General Graphs. Electronic Colloquium on Computational Complexity (ECCC), 18(101), 2011. URL: http://eccc.hpi-web.de/report/2011/101/.
  18. Angsheng Li and Pan Peng. Testing Small Set Expansion in General Graphs. In Proceedings of the 32nd International Symposium on Theoretical Aspects of Computer Science (STACS), 2015. Google Scholar
  19. Nathan Linial. Locality in distributed graph algorithms. SIAM Journal on Computing (SICOMP), 21(1), 1992. URL: http://dx.doi.org/10.1137/0221015.
  20. Alexander Lubotzky, Ralph Phillips, and Peter Sarnak. Ramanujan graphs. Combinatorica, 8(3), 1988. URL: http://dx.doi.org/10.1007/BF02126799.
  21. Anisur Rahaman Molla and Gopal Pandurangan. Distributed Computation of Mixing Time. In Proceedings of the 18th International Conference on Distributed Computing and Networking (ICDCN), 2017. Google Scholar
  22. Asaf Nachmias and Asaf Shapira. Testing the expansion of a graph. Information and Computation, 208(4), 2010. URL: http://dx.doi.org/10.1016/j.ic.2009.09.002.
  23. Uwe Naumann and Olaf Schenk, editors. Combinatorial Scientific Computing. CRC Press, 2012. Google Scholar
  24. Alistair Sinclair. Algorithms for Random Generation and Counting: A Markov Chain Approach. Birkhauser Verlag, 1993. 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 Schloss Dagstuhl - LZI GmbH Imprint Privacy Contact