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A Two-Sided Error Distributed Property Tester For Conductance

Authors Hendrik Fichtenberger , Yadu Vasudev

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

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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.

Cite As Get 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

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.

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