Stochastic Distance in Property Testing
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916330261708800 |
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| author | Meir, Uri Schwartzman, Gregory Yoshida, Yuichi |
| author_facet | Meir, Uri Schwartzman, Gregory Yoshida, Yuichi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14080 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Distance in Property Testing Meir, Uri Schwartzman, Gregory Yoshida, Yuichi Distributed, Parallel, and Cluster Computing 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. |
| title | Stochastic Distance in Property Testing |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2407.14080 |