## 3 System and Scenario Description  
In essence, the goal of any method for constructing multi-topology routing is to ensure that there are multiple transmission paths between a node pair. In traditional networks, switches are responsible for both data forwarding and control logic, which limits the flexibility of packet forwarding in a top-down manner. That is, multiple logical topologies are first established, and then, for each logical topology, the switches calculate the shortest path to each destination node based on the link weights in that topology and stores the results in the forwarding table. Each forwarding table corresponds to a logical topology. From this perspective, a logical topology corresponds to a single path for each node pair in the network. Software-defined networking is an emerging network architecture. It separates the control layer from the data layer of the network, providing a more flexible and programmable network management method. In SDN, switches are only responsible for packet forwarding, while the control logic is managed by the controller. An SDN controller installs packet forwarding rules in switches using protocols such as P4 [19] and OpenFlow [20] to control how data packets are processed. Each switch has one or more flow tables, and each flow table contains a set of flow entries, where each entry defines the matching conditions and actions for packet processing. The switch forwards packets according to these rules. Given the flexible forwarding characteristics of SDN, the controller can directly specify the path between two nodes in different logical topologies and install the corresponding flow forwarding rules as flow entries in the relevant switches. This eliminates the need for each router or switch in traditional networks to independently determine the path. As a result, this approach is more flexible, intelligent, and efficient, enabling rapid adaptation to dynamic traffic demands. Similarly, each flow table corresponds to a logical topology. In an SDN switch, flow tables are arranged in order. Data packets first match the flow table with the highest priority. After a data packet is processed in a flow table, it is forwarded to another flow table if the action is \"Goto Table\". This mechanism allows us to implement multi-topology routing in SDN. The controller generates multiple logical topologies based on the physical topology through certain strategies and installs the packet forwarding rules for each topology as flow entries in the relevant switches. Each switch stores multiple flow tables corresponding to each topology. In addition, there is a flow table with the highest priority known as the \"topology selection table\", which is configured for selecting topologies for mobile data flows. It is updated in the relevant switches when a mobility event occurs. In real-world networks, there are multiple mobile users that may connect to the network through different switches. Additionally, the content requested by users may vary, leading to different bandwidth and delay requirements. Flow Table 0 can change dynamically based on user demands and the network situation. It allocates topologies for the multiple data flows. By using a certain strategy to dynamically construct Flow Table 0, it can meet the requirements of multiple mobile users. While a multi-topology provides multiple paths, not all topologies must be used. The specific topologies to be used, and the assignment of data flows to these topologies, are determined by Flow Table 0. The construction of the topology selection table is not the focus of this paper. When a data packet enters a switch, it first matches the topology selection table, then proceeds to the corresponding flow table for forwarding. Figure 1 shows an example of multi-topology routing in SDN and the processing logic in a switch. As shown in Figure 1, there are four switches. The black connections represent the physical topology. The red connections represent Logical Topology 1, and the yellow connections represent Logical Topology 2.