Learning Very Large Graphs and Nonsingular Actions of Discrete Groups

08/27/2019

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by   Gábor Elek, et al.

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Recently, Goldreich introduced the notion of property testing of bounded-degree graphs with an unknown distribution. We propose a slight modification of his idea: the Radon-Nikodym Oracles. Using these oracles, any reasonable graph property can be tested against any reasonable distribution in the category of planar graphs. We also discuss Randomized Local Distributed Algorithms, which work on very large graphs with unknown distributions. Also, this note is an attempt to explain the intimate relation in between this property testing model and the ergodic theory of nonsingular actions of discrete groups, in particular, hyperfinite actions.