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Federated learning (FL) is a promising machine learning approach for Internet of Things (IoT), but it has to address network congestion problems when the population of IoT devices grows. Hierarchical FL (HFL) alleviates this issue by distributing model aggregation to multiple edge servers. Nevertheless, the challenge of communication overhead remains, especially in scenarios where all IoT devices simultaneously join the training process. For scalability, practical HFL schemes select a subset of IoT devices to participate in the training, hence the notion of device scheduling. In this setting, only selected IoT devices are scheduled to participate in the global training, with each of them being assigned to one edge server. Existing HFL assignment methods are primarily based on search mechanisms, which suffer from high latency in finding the optimal assignment. This article proposes an improved -center algorithm …