Four fault-free $B_{n-2}$'s in $B_{n}$ under the random node fault model
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910589120413696 |
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| author | Meng, KaiYue Yang, Yuxing |
| author_facet | Meng, KaiYue Yang, Yuxing |
| contents | Let $n\geq 4$. Each $B_{n-2}$ in $B_n$ has one of the forms $a_1a_2X^{n-2}$, $a_1X^{n-2}a_2$ and $X^{n-2}a_1a_2$. Let $1-p$ be the fault probiability of each node in the $n$-dimensional bubble-sort network $B_{n}$ under the random node fault model. In this paper, we determine the probability that there are four distinct fault-free $B_{n-2}$'s in $B_{n}$ by considering all possible combinatorial cases of the four fault-free $B_{n-2}$'s. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Four fault-free $B_{n-2}$'s in $B_{n}$ under the random node fault model Meng, KaiYue Yang, Yuxing Combinatorics 05C90 Let $n\geq 4$. Each $B_{n-2}$ in $B_n$ has one of the forms $a_1a_2X^{n-2}$, $a_1X^{n-2}a_2$ and $X^{n-2}a_1a_2$. Let $1-p$ be the fault probiability of each node in the $n$-dimensional bubble-sort network $B_{n}$ under the random node fault model. In this paper, we determine the probability that there are four distinct fault-free $B_{n-2}$'s in $B_{n}$ by considering all possible combinatorial cases of the four fault-free $B_{n-2}$'s. |
| title | Four fault-free $B_{n-2}$'s in $B_{n}$ under the random node fault model |
| topic | Combinatorics 05C90 |
| url | https://arxiv.org/abs/2409.02585 |