## 5 Comparison of Algorithm Performance
### Performance Comparison  
The survivability and fault tolerance of a network are critical metrics for assessing the ability of a communication network to maintain its functionality and performance in the face of various external threats and internal failures. These attributes are particularly  
Figure 10: Topology of air–sea cross-domain communication networks with deliberate attack.  
crucial for air-sea cross-domain communication networks, which often operate in complex and dynamic environments and are subject to a diverse range of threat sources. Both survivability and fault tolerance refer to the network's capacity to continue functioning and provide services despite attacks, failures, or other anomalous conditions.  
In this study, the maximum connectivity ratio (C) is selected as the key performance metric, defined as the ratio of the number of nodes in the largest connected subgraph to the total number of nodes in the network, as shown in Equation (27). This metric quantifies the ability of the network to maintain connectivity after node failures and reflects the resilience and recovery capability of the network under partial node failures. By comparing the results of different algorithms under random failure and deliberate attack scenarios, this paper aims to assess the effectiveness of each algorithm in maintaining and restoring network connectivity, thereby providing a basis for selecting the optimal recovery strategy.  
\[C=\frac{n^{\prime}}{n}, \tag{27}\]  
where \(n^{\prime}\) is the number of nodes of the most connected subgraph, and \(n\) represents the total number of nodes in the air-sea cross-domain communication network.  
Next, we compare the maximum network connectivity of the proposed algorithm with that of the unpredicted shortest path recovery algorithm and the one-hop neighbor link prediction recovery algorithm, as shown in Figure 11. It can be seen that the maximum network connectivity ratio of the three algorithms decreases with the increase in the proportion of failed nodes. The proposed algorithm comprehensively considers the connectivity restoration between all affected nodes, so it can maintain the connectivity of the network when the proportion of failed nodes is small. Its performance in network connectivity recovery is better than that of the other two classical algorithms.  
As illustrated in Figure 12, the change in the maximum network connectivity under different node failure scales is presented. It is evident that as the proportion of failed nodes increases, the maximum connectivity ratio of all three algorithms decreases. In comparison with Figure 11, the network connectivity of the unpredicted shortest path recovery algorithm and the one-hop neighbor link prediction recovery algorithm decreases more significantly. This is due to the malicious nature of deliberate attacks, which specifically target nodes of higher importance within the network, resulting in more severe network damage compared to random failures. The proposed improved Dijkstra-load-balancing algorithm demonstrates superior fault tolerance compared to both the no-prediction shortest path recovery algorithm and the one-hop neighbor link prediction recovery algorithm. When  
Figure 11: The maximum network connectivity in random failure scenarios.  
the proportion of failed nodes is less than 0.4, this algorithm is capable of maintaining the overall network connectivity. Furthermore, as the failure rate increases, the decline in connectivity is more gradual, outperforming the other two algorithms.