The ultra-low latency requirements of 5G/6G applications and privacy constraints call for distributed machine learning systems to be deployed at the edge. With its simple yet effective approach, federated learning (FL) is a natural solution for massive user-owned devices in edge computing with distributed and private training data. FL methods based on FedAvg typically follow a naive star topology, ignoring the heterogeneity and hierarchy of the volatile edge computing architectures and topologies in reality. Several other network topologies exist and can address the limitations and bottlenecks of the star topology. This motivates us to survey network topology-related FL solutions. In this paper, we conduct a comprehensive survey of the existing FL works focusing on network topologies. After a brief overview of FL and edge computing networks, we discuss various edge network topologies as well as their advantages and disadvantages. Lastly, we discuss the remaining challenges and future works for applying FL to topology-specific edge networks.
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