## 3 DC-SoC Consortium Chain Network Model
### Initial Clustering
However, this approach often results in a high sampling rate, unnecessary as the identification of cluster classes and construction of propagation structures typically do not require many core objects. Therefore, DBSCAN++ approximates the K-center algorithm through the use of a greedy initialization method. In this method, the peer with the highest latency from the current input peer is consistently selected during the core peer search and added to the set \(S\) until the number of peers in \(S\) meets the specified parameter \(m\). The value of the parameter \(m\) is determined based on specific circumstances. Subsequently, peers in the set \(S\) are traversed to identify the core peer and its neighborhood, ensuring the computation process for high overhead density stays within \(m\) iterations. Lastly, the remaining outliers are incorporated into the neighborhood of the nearest core object via a KD tree. In conclusion, DBSCAN++ leverages the idea of K-center to reduce the sampling rate of core objects while maintaining effective neighborhood coverage in the space. Its time complexity is \(O(nm)\), where \(n\) represents the total number of peers. Figure 2 illustrates the schematic diagram of the peer clustering process in DC-SoC. The DBSCAN++ algorithm enhances the clustering process within DC-SoC by optimizing the sampling of core objects while ensuring comprehensive neighborhood coverage. In traditional decentralized systems, establishing an optimal network structure is essential for efficient block propagation. DBSCAN++ reduces the computational overhead typically associated with high-dimensional clustering, while also improving scalability and minimizing latency in the network. Specifically, the algorithm employs a greedy initialization technique that approximates the K-center method, dynamically selecting core nodes based on their network latency to neighboring peers. This dynamic selection process facilitates faster clustering, particularly in environments with large and constantly changing sets of peers. In a decentralized context, where nodes frequently leave or join the network, DC-SoC incorporates a real-time dynamic clustering maintenance mechanism to ensure continuous network stability. When nodes become inactive or new nodes request to join, the system detects these changes and adjusts cluster configurations in real-time. For newly joining nodes, the algorithm assigns them to the nearest cluster based on a proximity-based metric, such as the Euclidean distance to the cluster's core node. If a core node becomes  
Figure 2: The process of density clustering. inactive, the algorithm triggers an election process to select a new core node from the remaining cluster members, evaluated by their trustworthiness and performance within the network. Additionally, the system periodically checks cluster integrity to prevent cluster fragmentation or underutilization. If a cluster becomes too small or loses cohesion, it is integrated with a nearby cluster to maintain optimal propagation efficiency and network stability. This dynamic process ensures that DC-SoC sustains a resilient cluster architecture, even in highly dynamic environments with frequent changes in node availability. The specific process is detailed in Algorithm 1.