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arXiv 2412.04771cs.DCcs.DS
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覆盖网络构建:改进的总体与逐节点消息复杂度

Overlay Network Construction: Improved Overall and Node-Wise Message Complexity

Yi-Jun Chang, Yanyu Chen, Gopinath Mishra

AI总结:

研究分布式覆盖网络构建问题,在GOSSIP-reply和HYBRID两种模型下提出WFT构建协议,实现了O(n log n)的消息复杂度和对数级的轮数开销。

摘要:

我们考虑构建分布式覆盖网络的问题,其中可重构系统中的节点可以与已知标识符的节点建立或断开连接。初始时,每个节点仅知道自身及其邻居的标识符,形成局部通道,而不断演化的结构被称为全局通道。目标是将任意连通图重配置为所需拓扑,例如有界度扩展图或具有常数最大度和对数直径的良构树(WFT),同时最小化总轮数和消息复杂度。该问题反映了现实世界中对等网络构建,旨在创建稳健且高效的系统。\n我们在由$n$个节点组成的网络中,在两种模型下研究覆盖网络重构问题:\textsf{GOSSIP-reply}{}和\textsf{HYBRID}{}。在\textsf{GOSSIP-reply}{}模型中,每个节点可以在一轮中发送一条消息并接收相应的回复消息。在\textsf{HYBRID}{}模型中,节点可以在局部通道中向每个邻居发送$O(1)$条消息,并在全局通道中总共发送$O(\log n)$条消息。\n在两种模型中,我们提出了使用$O(\log n)$位消息进行WFT构建的协议,其消息复杂度为$O\left(n \log n\right)$。在\textsf{GOSSIP-reply}{}模型中,我们的协议需要$O(\log n)$轮,而在\textsf{HYBRID}{}模型中,我们的协议需要$O(\log^2 n)$轮。两种协议均使用$O\left(n \log^2 n\right)$位的通信开销。

英文摘要:

We consider the problem of constructing distributed overlay networks, where nodes in a reconfigurable system can create or sever connections with nodes whose identifiers they know. Initially, each node knows only its own and its neighbors' identifiers, forming a local channel, while the evolving structure is termed the global channel. The goal is to reconfigure any connected graph into a desired topology, such as a bounded-degree expander graph or a well-formed tree (WFT) with a constant maximum degree and logarithmic diameter, minimizing the total number of rounds and message complexity. This problem mirrors real-world peer-to-peer network construction, where creating robust and efficient systems is desired. We study the overlay reconstruction problem in a network of $n$ nodes in two models: \textsf{GOSSIP-reply}{} and \textsf{HYBRID}{}. In the \textsf{GOSSIP-reply}{} model, each node can send a message and receive a corresponding reply message in one round. In the \textsf{HYBRID}{} model, a node can send $O(1)$ messages to each neighbor in the local channel and a total of $O(\log n)$ messages in the global channel. In both models, we propose protocols for WFT construction with $O\left(n \log n\right)$ message complexities using messages of $O(\log n)$ bits. In the \textsf{GOSSIP-reply}{} model, our protocol takes $O(\log n)$ rounds while in the \textsf{HYBRID} model, our protocol takes $O(\log^2 n)$ rounds. Both protocols use $O\left(n \log^2 n\right)$ bits of communication.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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