Stochastic Distance in Property Testing
Uri Meir, Gregory Schwartzman, Yuichi Yoshida

TL;DR
This paper introduces stochastic distance, a probabilistic measure for property testing, which is particularly effective in distributed settings, enabling ultra-fast algorithms for properties like k-edge-connectivity.
Contribution
The paper proposes stochastic distance as a new concept for property testing and demonstrates its effectiveness in designing fast distributed algorithms for graph properties.
Findings
Stochastic distance aligns with probabilistic edge addition.
Efficient distributed testers for k-edge-connectivity.
New framework for property testing in distributed models.
Abstract
We introduce a novel concept termed "stochastic distance" for property testing. Diverging from the traditional definition of distance, where a distance implies that there exist edges that can be added to ensure a graph possesses a certain property (such as -edge-connectivity), our new notion implies that there is a high probability that adding random edges will endow the graph with the desired property. While formulating testers based on this new distance proves challenging in a sequential environment, it is much easier in a distributed setting. Taking -edge-connectivity as a case study, we design ultra-fast testing algorithms in the CONGEST model. Our introduction of stochastic distance offers a more natural fit for the distributed setting, providing a promising avenue for future research in emerging models of computation.
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