Learning Very Large Graphs with Unknown Vertex Distributions

TL;DR

This paper introduces Radon-Nikodym Oracles for constant-time property testing of large planar graphs with unknown distributions, and explores distributed algorithms and learning methods based on observations.

Contribution

It proposes Radon-Nikodym Oracles for efficient property testing on large graphs with unknown distributions, extending previous work to broader graph classes and methods.

Findings

Property testing in constant time for planar graphs with unknown distributions

Radon-Nikodym Oracles enable efficient testing of graph properties

Discussion of distributed algorithms and learning from observations

Abstract

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 in constant-time against any reasonable unknown distribution in the category of planar graphs. We also discuss Randomized Local Distributed Algorithms, which work on very large graphs with unknown distributions. Finally, we discuss how can we learn graph properties using observations instead of samplings.