This paper addresses the cornerstone family of local problems in distributed computing, and investigates the curious gap between randomized and deterministic solutions under bandwidth restrictions. Our main contribution is in providing tools for derandomizing solutions to local problems, when the n nodes can only send $$O(\log n)$$ O ( log n ) -bit messages in each round of communication. Our framework mostly follows by the derandomization approach of Luby (J Comput Syst Sci 47(2):250–286, 1993) combined with the power of all to all communication. Our key results are as follows: first, we show that in the congested clique model, which allows all-to-all communication, there is a deterministic maximal independent set algorithm that runs in $$O(\log ^2 {\varDelta })$$ O ( log 2 Δ ) rounds, where $${\varDelta }$$ Δ is the maximum degree. When $${\varDelta }=O(n^{1/3})$$ Δ = O ( n 1 / 3 ) , the bound improves to $$O(\log {\varDelta })$$ O ( log Δ ) . In addition, we deterministically construct a $$(2k-1)$$ ( 2 k - 1 ) -spanner with $$O(kn^{1+1/k}\log n)$$ O ( k n 1 + 1 / k log n ) edges in $$O(k \log n)$$ O ( k log n ) rounds in the congested clique model.

中文翻译：

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在带宽限制下对局部分布式算法进行去随机化

本文解决了分布式计算中局部问题的基石系列，并研究了在带宽限制下随机和确定性解决方案之间的奇怪差距。我们的主要贡献是为本地问题的去随机化解决方案提供工具，当 n 个节点在每轮通信中只能发送 $$O(\log n)$$ O ( log n ) 位消息时。我们的框架主要遵循 Luby (J Comput Syst Sci 47(2):250–286, 1993) 的去随机化方法，并结合了所有人对所有人的交流能力。我们的主要结果如下：首先，我们证明了在拥塞团模型中，它允许全对全通信，有一个确定性的最大独立集算法，它运行在 $$O(\log ^2 {\varDelta } )$$ O ( log 2 Δ ) 轮，其中 $${\varDelta }$$ Δ 是最大度数。当 $${\varDelta }=O(n^{1/3})$$ Δ = O ( n 1 / 3 ) 时，界限提高到 $$O(\log {\varDelta })$$ O ( log △)。此外，我们确定性地构造了一个 $$(2k-1)$$ ( 2 k - 1 ) -spanner 与 $$O(kn^{1+1/k}\log n)$$ O ( kn 1 + 1 / k log n ) 在拥塞团模型中的 $$O(k \log n)$O ( k log n ) 轮中的边。