This paper explores the distributed broadcast problem within the context of network communications, a critical challenge in decentralized information dissemination. We put forth a novel hypergraph-based approach to address this issue, focusing on minimizing the number of broadcasts to ensure comprehensive data sharing among all network users. A key contribution of our work is the establishment of a general lower bound for the problem using the min-cut capacity of hypergraphs. Additionally, we present the distributed broadcast for quasi-trees (DBQT) algorithm tailored for the unique structure of quasi-trees, which is proven to be optimal. This paper advances both network communication strategies and hypergraph theory, with implications for a wide range of real-world applications, from vehicular and sensor networks to distributed storage systems.

翻译：本文探讨了网络通信背景下的分布式广播问题，这是去中心化信息传播中的一项关键挑战。我们提出了一种新颖的基于超图的方法来解决该问题，重点在于最小化广播次数，以确保所有网络用户之间的全面数据共享。我们工作的一个关键贡献是利用超图的最小割容量，为这一问题建立了通用下界。此外，我们提出了适用于准树独特结构的分布式广播算法（DBQT），并证明了其最优性。本文推进了网络通信策略与超图理论的发展，对从车载网络、传感器网络到分布式存储系统等广泛的现实应用具有重要启示。