We study the role of randomness in the broadcast congested clique model. This is a message-passing model of distributed computation where the nodes of a network know their local neighborhoods and they broadcast, in synchronous rounds, messages that are visible to every other node.

This works aims to separate three different settings: deterministic protocols, randomized protocols with private coins, and randomized protocols with public coins. We obtain the following results:

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If more than one round is allowed, public randomness is as powerful as private randomness.

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One-round public-coin algorithms can be exponentially more powerful than deterministic algorithms running in several rounds.

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One-round public-coin algorithms can be exponentially more powerful than one-round private-coin algorithms.

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One-round private-coin algorithms can be exponentially more powerful than one-round deterministic algorithms.

我们研究随机性在广播拥挤集团模型中的作用。这是分布式计算的消息传递模型，其中网络节点知道它们的本地邻域，并且它们以同步轮次广播对每个其他节点可见的消息。

这项工作旨在分离三种不同的设置：确定性协议、带有私人硬币的随机协议和带有公共硬币的随机协议。我们得到以下结果：

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如果允许多于一轮，则公共随机性与私有随机性一样强大。

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一轮公开币算法比在几轮中运行的确定性算法更强大。

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一轮公共硬币算法可以比一轮私人硬币算法强大得多。

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一轮私人硬币算法可以比一轮确定性算法强大得多。