Testing properties of graphs and functions

TL;DR

This paper introduces an analytic approach to graph property testing by examining symmetric functions through sampling, extending large graph results, and applying findings to classical graph theory problems.

Contribution

It develops an analytic framework for graph property testing and characterizes testable properties, bridging the gap between function-based and graph-based testing.

Findings

Characterization of testable properties in the analytic setting

Extension of large graph results to the new framework

Applicability of results to classical graph property testing

Abstract

We define an analytic version of the graph property testing problem, which can be formulated as studying an unknown 2-variable symmetric function through sampling from its domain and studying the random graph obtained when using the function values as edge probabilities. We give a characterization of properties testable this way, and extend a number of results about ``large graphs'' to this setting. These results can be applied to the original graph-theoretic property testing.