A Hypergraph Approach to Distributed Broadcast

2024-04-25

arXiv.org

AI Summary

This paper addresses the broadcast optimization problem in distributed networks, aiming to minimize the number of broadcast rounds required for global data dissemination—applicable to vehicular ad hoc networks, wireless sensor networks, and distributed storage systems. Methodologically, it introduces a novel hypergraph-based modeling framework and establishes, for the first time, a theoretical lower bound on broadcast rounds via the minimum cut capacity of the underlying hypergraph. For networks with quasi-tree topology, the authors propose a distributed broadcast algorithm, DBQT, and rigorously prove its round-optimality and tightness with respect to the derived lower bound. By integrating hypergraph representation, quasi-tree structural analysis, and min-cut theory, DBQT achieves provably optimal communication efficiency in quasi-tree networks, substantially reducing communication overhead compared to existing approaches.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

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. The key contributions of this work include the establishment of a general lower bound for the problem using the min-cut capacity of hypergraphs, and a 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.

Problem

• Distributed broadcast problem in network communications
• Minimizing broadcasts for comprehensive data sharing
• Establishing lower bound using hypergraph min-cut capacity

Innovation

• Hypergraph-based approach for distributed broadcast
• Minimizing broadcasts using min-cut capacity
• Optimal DBQT algorithm for quasi-trees