Federated learning (FL), which addresses data privacy issues by training models on resource-constrained mobile devices in a distributed manner, has attracted significant research attention. However, the problem of optimizing FL client selection in mobile federated learning networks (MFLNs), where devices move in and out of each others' coverage and no FL server knows all the data owners, remains open. To bridge this gap, we propose a first-of-its-kind \underline{Soc}ially-aware \underline{Fed}erated \underline{C}lient \underline{S}election (SocFedCS) approach to minimize costs and train high-quality FL models. SocFedCS enriches the candidate FL client pool by enabling data owners to propagate FL task information through their local networks of trust, even as devices are moving into and out of each others' coverage. Based on Lyapunov optimization, we first transform this time-coupled problem into a step-by-step optimization problem. Then, we design a method based on alternating minimization and self-adaptive global best harmony search to solve this mixed-integer optimization problem. Extensive experiments comparing SocFedCS against five state-of-the-art approaches based on four real-world multimedia datasets demonstrate that it achieves 2.06\% higher test accuracy and 12.24\% lower cost on average than the best-performing baseline.
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