We focus on designing Peer-to-Peer (P2P) networks that enable efficient communication. Over the last two decades, there has been substantial algorithmic research on distributed protocols for building P2P networks with various desirable properties such as high expansion, low diameter, and robustness to a large number of deletions. A key underlying theme in all of these works is to distributively build a \emph{random graph} topology that guarantees the above properties. Moreover, the random connectivity topology is widely deployed in many P2P systems today, including those that implement blockchains and cryptocurrencies. However, a major drawback of using a random graph topology for a P2P network is that the random topology does not respect the \emph{underlying} (Internet) communication topology. This creates a large \emph{propagation delay}, which is a major communication bottleneck in modern P2P networks. In this paper, we work towards designing P2P networks that are communication-efficient (having small propagation delay) with provable guarantees. Our main contribution is an efficient, decentralized protocol, $\textsc{Close-Weaver}$, that transforms a random graph topology embedded in an underlying Euclidean space into a topology that also respects the underlying metric. We then present efficient point-to-point routing and broadcast protocols that achieve essentially optimal performance with respect to the underlying space.

翻译：本文聚焦于设计能够实现高效通信的对等网络。过去二十年间，针对构建具有高扩展性、低直径以及对大量节点删除具有鲁棒性等理想特性的对等网络，已有大量关于分布式协议的算法研究。这些工作的一个核心主题是分布式地构建一种能够保证上述特性的随机图拓扑。此外，这种随机连接拓扑已广泛应用于当今许多对等系统中，包括实现区块链和加密货币的系统。然而，在对等网络中使用随机图拓扑的一个主要缺陷在于，随机拓扑未能充分考虑底层通信拓扑，这导致了巨大的传播延迟，成为现代对等网络中的主要通信瓶颈。本文致力于设计具有可证明保证的通信高效型对等网络。我们的主要贡献是提出了一种高效的分布式协议 $\textsc{Close-Weaver}$，该协议能够将嵌入底层欧几里得空间的随机图拓扑转换为同时尊重底层度量的拓扑。随后，我们提出了高效的点对点路由和广播协议，这些协议在底层空间上实现了近乎最优的性能。