## 4 Problem Modeling and Solution
### Logical Topologies Construction
This means that the transmission capacity from the source node to the destination nodes along the discarded paths cannot be maximized. In contrast, other algorithms that select all paths from the source to those destination, while still respecting the flow entry constraints of the switches, could potentially offer higher transmission capacity between the source node and those destinations. However, such algorithms may consume more flow entry capacity, which restricts their ability to include paths for other destination nodes. This could result in imbalanced resource distribution across the network. ## 6 Conclusions

This paper presents a method for constructing a multi-topology to provide efficient switching paths for mobile data flows in software-defined networking (SDN). We proposed a multi-topology deployment scheme tailored for SDN. Additionally, we modeled the multi-topology construction problem with the objective of maximizing the average transmission capacity from the source node to each destination node. To solve this problem, we developed a method consisting of two algorithms. To evaluate its performance, we implemented the method in Mininet and compared it against existing solutions, including AMPLE, the k-shortest paths method, and the single-path switching method. The simulation results show that our method consistently outperforms the alternatives across key performance metrics. It reduces the average packet delay, lowers the packet loss rate, and improves throughput when a mobile device moves to different access switches. These results highlight the effectiveness of our approach in providing multiple efficient paths to each possible destination node and in balancing the transmission capacity across them. In future work, we will explore the dynamic management of a multi-topology. We plan to monitor current mobile devices' demands and network conditions at regular intervals. Based on these data, we will adjust the multi-topology accordingly. For example, we will increase the number of paths from the source node to destination nodes with high device density. We will also discard paths related to link or node failures and select alternative paths. Additionally, we will investigate efficient dynamic mobile data flow allocation algorithms to handle real-time network traffic and varying link conditions. Ultimately, we aim to develop more robust and optimized multipath routing solutions. \[\sum\limits_{p_{i}\in PT_{n}}x_{p_{i}}\leq c_{n},\quad\forall n\in N \tag{10}\]0 Comparison of throughput among different methods when the device moves to S1, S10, and S12. **Author Contributions:** Conceptualization, C.Z. and R.H.; investigation, C.Z. ; methodology, C.Z. ; software, C.Z. ; validation, C.Z. ; writing--original draft preparation, C.Z. ; writing--review and editing, H.D. and R.H.; supervision, H.D. and R.H. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Basic and Frontier Exploration Project Independently Deployed by the Institute of Acoustics, Chinese Academy of Sciences: Research on Wide-Area RDMA Transmission Acceleration Technology Based on SEANet (Project No. JCQY202407). **Data Availability Statement:** All of the necessary data are included in the article. **Acknowledgments:** We would like to express our gratitude to [PERSON] and [PERSON] for their meaningful support for this work. **Conflicts of Interest:** The authors declare no conflicts of interest.