# An Accelerated Maximum Flow Algorithm with Prediction Enhancement in Dynamic LEO Networks
## 2 Related Work
### Software-Defined Satellite Networks  
To enhance the adaptability of satellite networks and reduce the computational load on individual satellites, the SDN framework has been seamlessly integrated into the satellite constellation, giving rise to the software-defined satellite network (SDSN) [28; 29; 30]. By capitalizing on the centralized management and programmability features of SDN, the SDSN establishes a foundation for holistic satellite network management. This is achieved through the separation of the control plane from the LEO forwarding plane, which enables more sophisticated monitoring of network conditions and more efficient resource allocation, as evidenced in [30].  
[PERSON] et al. [31] presented a comprehensive review of an SDN-centric satellite network architecture. This architecture uses at least three Geostationary Earth Orbit (GEO) satellites as controllers to improve both operational efficiency and fine-grained control across the entire satellite constellation. To overcome the limitations of existing satellite communication  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & **Characteristics** & **Advantages** & **Limitations** \\ \hline TEG [11] & Models the dynamic topology of satellite networks using time-based snapshots. & Captures temporal variation in connectivity; supports time-aware routing. & Ignores energy, processing, or bandwidth constraints. \\ \hline e-TEG [11] & Extends TEG by incorporating energy constraints using virtual arcs. & Addresses energy limitations enables energy-aware flow optimization. & Increased model complexity; computationally intensive. \\ \hline Ford-Fulkerson Algorithm [7] & Iteratively finds augmenting paths until no residual capacity exists. & Simple; guarantees max flow in integral capacity networks. & Slow for large or dynamic networks; recomputation required after topology changes. \\ \hline Dinic’s algorithm [8] & Uses layered networks and blocking flows for efficient maximum flow computation. & Lower time complexity \((\mathrm{O}(\mathrm{n^{2}m}))\), suitable for large-scale networks. & Assumes static topology; complex implementation. \\ \hline Learning-augmented maximum flow algorithm [9] & Uses predicted flow values to accelerate computation, leveraging prior knowledge. & Reduces augmentation steps; adapts to recurring flow patterns & Prediction quality affects stability. \\ \hline
0-1 Min-cost flow algorithm [17] & Solves min-cost flow under binary capacity and cost constraints. & Efficient for highly structured, restricted problems. & Not directly applicable to general or dynamic satellite topologies. \\ \hline Approximate flow algorithm [24; 25] & Computes approximate maximum flows for large-scale networks. & Fast computation; scalable to large networks. & Approximation error; less accurate in constrained or real-time settings. \\ \hline Near-linear flow algorithm [26] & maximum to achieve near-linear complexity. & Theoretically optimal for very large networks. & Assumes static input; lacks support for real-time adaptability. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of TEG/e-TEG models and representative maximum flow algorithms.  
systems, such as slow configuration and poor quality of service (QoS) guarantees, the software-defined framework for integrated space-terrestrial satellite communication has introduced flexible traffic engineering strategies and optimized QoS mechanisms.  
These advancements are further explored in related studies. Ref. [32] conducted a detailed analysis of SDN-based satellite networks with the aim of improving performance, while [33] delved into leveraging SDN for dynamic resource management within satellite constellations. Moreover, the integration of SDN with satellite networks, which significantly improves flexibility and scalability, is extensively discussed in [34], highlighting the potential of SDSNs in space communications.