License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2018.19
URN: urn:nbn:de:0030-drops-96019
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9601/
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Fichtenberger, Hendrik ; Vasudev, Yadu

A Two-Sided Error Distributed Property Tester For Conductance

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LIPIcs-MFCS-2018-19.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{fichtenberger_et_al:LIPIcs:2018:9601,
  author =	{Hendrik Fichtenberger and Yadu Vasudev},
  title =	{{A Two-Sided Error Distributed Property Tester For Conductance}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9601},
  URN =		{urn:nbn:de:0030-drops-96019},
  doi =		{10.4230/LIPIcs.MFCS.2018.19},
  annote =	{Keywords: property testing, distributed algorithms, conductance}
}

Keywords: property testing, distributed algorithms, conductance
Collection: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 27.08.2018

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