## 1 Introduction  
Recommender systems, which are crucial applications of machine learning algorithms [1], are utilized across various domains such as e-commerce, advertising and other online services. These systems typically rely on historical interaction data between users and items for training. However, frequent access to users' raw data during training raises privacy concerns [2]. Consequently, due to the federated learning (FL) paradigm's capability of privacy protection, the adoption of FL in recommendation algorithms has gained significant attention. Federated recommender systems (FRSs) allow users to keep their personal data locally and share only model parameters with low privacy sensitivity for global model training [3]. This strategy not only significantly strengthens the privacy protection capabilities of the system but also enables the training process to take place directly on end devices, effectively utilizing decentralized computation resources. Additionally, participants can collaborate with other data platforms to boost the recommendation performance while adhering to regulatory and privacy requirements. However, due to the high-frequency exchange of model data between clients and the server, the process is severely restricted by communication conditions such as limited channel bandwidth and network instabilities [4]. In FRSs, users' participation in training is often limited by their communication capabilities, which prolongs the model training cycle. Despite significant advancements in accelerating convergence for many existing FL algorithms, not all of them can be directly applied to FRSs. This is primarily due to the following reasons:  
* Limitation 1: Insufficient training of partial clients. FRSs require modeling both items and clients, with client models remaining local and updated using the latest item models from the server. Existing FL acceleration algorithms, such as [5; 6], select a subset of clients based on their computation and communication resources for federated training. However, these algorithms often neglect the training of user models for resource-constrained clients, which negatively affects their recommendation performance. * Limitation 2: Invalid assumption of always-open communication channels. Some existing FL acceleration algorithms [7; 8] require all clients to obtain the global model for local training and upload the correlation between their local updates and the global model to the server. The server makes decisions based on these correlations and notifies partial clients that need to upload their updated data. This process requires that the communication channels always maintain effectiveness, which contradicts the inherent randomness of communication channels. * Limitation 3: Complexity in modeling relationships among clients. The algorithms proposed in [9; 10] need the server to model the relationships among clients based on their updated data. In typical FL scenarios, clients upload data that have the same structure. However, in FRSs, the interactions between clients and items are highly complex, resulting in significant variations in the types of item models uploaded by different clients. This poses a challenge for modeling relationships between clients. To avoid these issues, we introduce a simple and flexible framework, Federated Recommendation Framework Integrating Communication and Computation (FedRecI2C), aimed at accelerating model convergence in FRSs. Given that only a subset of clients participates in federated training due to communication constraints, we hypothesize that a client with communication constraints can enhance its model by leveraging local idle computation resources and limited communication capabilities. Specifically, motivated by the communication channels involving downloading and uploading in FRSs, we consider two scenarios of communication constraints. See Figure 1 for an illustration. * Scenario I.