Broadcasting in random recursive dags
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916595969818624 |
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| author | Briend, Simon Devroye, Luc Lugosi, Gabor |
| author_facet | Briend, Simon Devroye, Luc Lugosi, Gabor |
| contents | A uniform $k$-{\sc dag} generalizes the uniform random recursive tree by picking $k$ parents uniformly at random from the existing nodes. It starts with $k$ ''roots''. Each of the $k$ roots is assigned a bit. These bits are propagated by a noisy channel. The parents' bits are flipped with probability $p$, and a majority vote is taken. When all nodes have received their bits, the $k$-{\sc dag} is shown without identifying the roots. The goal is to estimate the majority bit among the roots. We identify the threshold for $p$ as a function of $k$ below which the majority rule among all nodes yields an error $c+o(1)$ with $c<1/2$. Above the threshold the majority rule errs with probability $1/2+o(1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_01727 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Broadcasting in random recursive dags Briend, Simon Devroye, Luc Lugosi, Gabor Machine Learning Social and Information Networks A uniform $k$-{\sc dag} generalizes the uniform random recursive tree by picking $k$ parents uniformly at random from the existing nodes. It starts with $k$ ''roots''. Each of the $k$ roots is assigned a bit. These bits are propagated by a noisy channel. The parents' bits are flipped with probability $p$, and a majority vote is taken. When all nodes have received their bits, the $k$-{\sc dag} is shown without identifying the roots. The goal is to estimate the majority bit among the roots. We identify the threshold for $p$ as a function of $k$ below which the majority rule among all nodes yields an error $c+o(1)$ with $c<1/2$. Above the threshold the majority rule errs with probability $1/2+o(1)$. |
| title | Broadcasting in random recursive dags |
| topic | Machine Learning Social and Information Networks |
| url | https://arxiv.org/abs/2306.01727 |