eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-27
19:1
19:15
10.4230/LIPIcs.MFCS.2018.19
article
A Two-Sided Error Distributed Property Tester For Conductance
Fichtenberger, Hendrik
1
https://orcid.org/0000-0003-3246-5323
Vasudev, Yadu
2
https://orcid.org/0000-0001-7918-7194
TU Dortmund, Dortmund, Germany
Indian Institute of Technology Madras, Chennai, India
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol117-mfcs2018/LIPIcs.MFCS.2018.19/LIPIcs.MFCS.2018.19.pdf
property testing
distributed algorithms
conductance