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arXiv · 2407.14080

Stochastic Distance in Property Testing

Uri Meir·Gregory Schwartzman·Yuichi Yoshida
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Abstract

We introduce a novel concept termed "stochastic distance" for property testing. Diverging from the traditional definition of distance, where a distance $t$ implies that there exist $t$ edges that can be added to ensure a graph possesses a certain property (such as $k$-edge-connectivity), our new notion implies that there is a high probability that adding $t$ 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 $k$-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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Uri Meir, Gregory Schwartzman, Yuichi Yoshida. 2024-07-19. Stochastic Distance in Property Testing. https://arxiv.org/abs/2407.14080

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