## 4 Methodology
### Domain Clustering Based on Multi-Path Transmission
#### 4.2.1 Domain Clustering and Network Management  
In large-scale satellite networks, effectively managing resources and reducing network overhead is a critical problem. Existing methods often ignore changes in network topology and interdependencies between nodes, making them ill-suited for dynamic network environments. To address these challenges, our approach adopts an SDN-based domain clustering strategy. SDN enables centralized control and dynamic management, which is crucial for satellite networks characterized by frequently changing topologies and unstable connections. By partitioning the network into multiple logical domains (Domain Clusters, DCs), the SDN controller can obtain a global view of the network state, perform real-time re  
Figure 2: SDN-based domain clustering and collaborative scheduling framework. source scheduling, and optimize path selection. This centralized management significantly reduces the network control overhead, improves response times, and enhances overall network stability, while also facilitating rapid detection and mitigation of network anomalies. Accordingly, this paper proposes a domain clustering scheme based on a hierarchical control mechanism (SDN), which divides the satellite network into multiple logical domains, where the nodes within each domain coordinate and communicate with each other to efficiently manage inter-node communication and further reduce the control overhead. Suppose there are \(N\) satellite nodes in the network, and each node can choose to join a different domain \(D_{i}\), where the link reliability represents the reliability of the link between nodes \(R_{ij}\). This paper introduces a weighted objective function to optimize the node assignment strategy, to maximize the network's reliability and overhead balance:  
\[\min_{D}\biggl{[}\lambda(1-R)+(1-\lambda)\cdot\frac{\eta_{\text{total}}}{\eta_ {\text{max}}}\biggr{]} \tag{29}\]  
where \(R\) is the path reliability, \(\eta_{\text{total}}\) is the total network overhead, \(\eta_{\text{max}}\) is the maximum overhead standard, and \(\lambda\) is the weighting factor. Regarding a performance comparison with other hierarchical clustering mechanisms, such as federated-learning-based adaptive clustering for resource allocation, our study specifically addresses the challenges of dynamically unstable network connections. Federated learning methods typically rely on stable communication links for consistent model aggregation and convergence. In our dynamic satellite network scenario, where connections are frequently disrupted, federated learning may suffer from discontinuous model updates, leading to unstable training outcomes and poor convergence. Additionally, the inherent lack of explainability in federated learning models further complicates real-time fault diagnosis and adjustment. In contrast, the SDN-based domain clustering approach leverages centralized control and real-time network state monitoring, making it more robust and efficient for resource allocation in such environments. In the domain clustering process, the utility function of each node is used to describe its performance within the selected domain. For node \(i\) belonging to domain \(D_{k}\), the utility function can be defined as  
\[U_{i}=\frac{1}{1+\alpha\cdot d_{i}^{2}}\cdot\sum_{j\in D_{k}}R_{ij} \tag{30}\]  
where \(d_{i}\) is the distance from node \(i\) to the center of its assigned domain, \(\alpha\) is the adjustment factor, and \(R_{ij}\) is the link reliability between node \(i\) and other nodes \(j\) in the domain. This utility function considers both the node's distance and link reliability. In dynamic satellite networks, the hierarchical control-based domain clustering method can effectively improve network reliability and performance in the context of multi-path transmission and cluster head election. Proof. : To prove this theorem, we first calculate the utility function for each node \(i\) and optimize the node assignment according to the objective function.