# An Accelerated Maximum Flow Algorithm with Prediction Enhancement in Dynamic LEO Networks
## 6 Conclusions and Future Work  
In this paper, we introduced a predictive acceleration algorithm for solving the maximum flow problem in LEO satellite networks. By leveraging a predictive warm-start  
Figure 8: Acceleration performance of predictive LEO maximum flow with varying satellite storage capacities.  
Figure 9: Acceleration performance of predictive LEO maximum flow with a varying network scale.  
approach, our algorithm significantly enhances the efficiency of traditional flow algorithms, enabling faster recalculations of maximum flow in dynamic, resource-constrained environments.  
Our extensive evaluation demonstrated that the predictive flow acquisition mechanism, along with the warm-starting Ford-Fulkerson approach, delivers substantial acceleration in maximum flow computation, especially under varying network scales and storage constraints. The proposed predictive LEO maximum flow algorithm consistently outperforms existing methods such as Dinic's algorithm, MPTPT-based routing, and the e-TEG algorithm, particularly in terms of computational efficiency. The acceleration percentages achieved by the proposed algorithm, especially in scenarios with constrained satellite storage, highlight the algorithm's ability to optimize flow allocation while respecting dynamic network conditions.  
In the future, we will aim to further optimize the pathfinding process to enhance real-time responsiveness in large-scale satellite networks. Currently, we use BFS for predictive flow acquisition, which has a time complexity of \(O(V+E)\). While the proposed warm-starting FF and predictive LEO maximum flow algorithms already demonstrate superior time efficiency compared to existing methods, full BFS may introduce non-negligible overhead in scenarios involving larger constellations or more frequent topology changes. Therefore, we plan to further reduce BFS overhead and enhance computational speed. One direction for improvement could involve integrating advanced data structures, such as dynamic tree architectures, to streamline path optimization. We also plan to investigate depth-limited or priority-guided BFS strategies that can reduce search overhead while preserving accuracy. Furthermore, we plan to incorporate machine learning-based traffic prediction models, such as temporal graph neural networks and adaptive reinforcement learning strategies, to improve the accuracy and responsiveness of flow forecasting in dynamic satellite networks. Finally, we will develop distributed computing paradigms to ensure scalability for mega-constellation deployments.  
Conceptualization, J.S. and X.W.; Methodology, X.G. and X.W.; Software, J.S. and F.Y.; Validation, J.S. and X.G.; Formal analysis, J.S., X.G. and F.Y.; Investigation, X.W.; Resources, F.Y. and X.W.; Writing--original draft, J.S.; Writing--review & editing, X.G.; Visualization, J.S.; Supervision, X.G.; Project administration, X.G. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Not applicable. Not applicable. Data Availability Statement The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author. The authors declare no conflicts of interest.