Computing in a Faulty Congested Clique
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Censor-Hillel, Keren Soto, Pedro |
| author_facet | Censor-Hillel, Keren Soto, Pedro |
| contents | We study a Faulty Congested Clique model, in which an adversary may fail nodes in the network throughout the computation. We show that any task of $O(n\log{n})$-bit input per node can be solved in roughly $n$ rounds, where $n$ is the size of the network. This nearly matches the linear upper bound on the complexity of the non-faulty Congested Clique model for such problems, by learning the entire input, and it holds in the faulty model even with a linear number of faults.
Our main contribution is that we establish that one can do much better by looking more closely at the computation. Given a deterministic algorithm $\mathcal{A}$ for the non-faulty Congested Clique model, we show how to transform it into an algorithm $\mathcal{A}'$ for the faulty model, with an overhead that could be as small as some logarithmic-in-$n$ factor, by considering refined complexity measures of $\mathcal{A}$.
As an exemplifying application of our approach, we show that the $O(n^{1/3})$-round complexity of semi-ring matrix multiplication [Censor-Hillel, Kaski, Korhonen, Lenzen, Paz, Suomela, PODC 2015] remains the same up to polylog factors in the faulty model, even if the adversary can fail $99\%$ of the nodes (or any other constant fraction). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11430 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing in a Faulty Congested Clique Censor-Hillel, Keren Soto, Pedro Data Structures and Algorithms Distributed, Parallel, and Cluster Computing We study a Faulty Congested Clique model, in which an adversary may fail nodes in the network throughout the computation. We show that any task of $O(n\log{n})$-bit input per node can be solved in roughly $n$ rounds, where $n$ is the size of the network. This nearly matches the linear upper bound on the complexity of the non-faulty Congested Clique model for such problems, by learning the entire input, and it holds in the faulty model even with a linear number of faults. Our main contribution is that we establish that one can do much better by looking more closely at the computation. Given a deterministic algorithm $\mathcal{A}$ for the non-faulty Congested Clique model, we show how to transform it into an algorithm $\mathcal{A}'$ for the faulty model, with an overhead that could be as small as some logarithmic-in-$n$ factor, by considering refined complexity measures of $\mathcal{A}$. As an exemplifying application of our approach, we show that the $O(n^{1/3})$-round complexity of semi-ring matrix multiplication [Censor-Hillel, Kaski, Korhonen, Lenzen, Paz, Suomela, PODC 2015] remains the same up to polylog factors in the faulty model, even if the adversary can fail $99\%$ of the nodes (or any other constant fraction). |
| title | Computing in a Faulty Congested Clique |
| topic | Data Structures and Algorithms Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2505.11430 |