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- W4379474815 abstract "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 $1/2+o(1)$." @default.
- W4379474815 created "2023-06-07" @default.
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- W4379474815 date "2023-06-02" @default.
- W4379474815 modified "2023-10-18" @default.
- W4379474815 title "Broadcasting in random recursive dags" @default.
- W4379474815 doi "https://doi.org/10.48550/arxiv.2306.01727" @default.
- W4379474815 hasPublicationYear "2023" @default.
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