# Adaptive Network Routing Technology for Near-Moon Space Cross-Domain Transmission
## 3 Routing Scheduling Algorithm
### Hierarchical Domain Value Routing Search  
In cross-domain hybrid topology networks, due to the high complexity of the overall architecture and the constantly changing local areas, there is great uncertainty in prediction. At the same time, routing search increases rapidly with the increase in the number of nodes and communication loads. This section presents a hierarchical routing search method for cross-domain networks. Based on the predicted communication rate between nodes, a hierarchical search strategy is designed. Compared to the traditional pre-planned search method used in fixed topology sub-networks to obtain the local optimal path, and combined with the random search method used in time-varying topology structures to obtain the optimal path between fixed topology sub-networks, this paper presents a unified search architecture.  
The routing search process is mainly divided into the following 5 steps:  
Step 1: The routing purpose is to transmit the communication payload \(q_{v,start}\) from node \(q_{v,start}\) to node \(q_{v,end}\) through node \(q_{v,end}\), with a maximum routing delay time constraint of \(\Delta_{\text{max}}\) and a maximum number of routing hops constraint of \(\Phi_{\text{max}}\), a minimum communication rate of \(F_{\text{min}}\) during link transmission, a task start time of \(t_{start}\), and a task end time of \(t_{end}=t_{start}+\Delta\) (\(\Delta\leq\Delta_{\text{max}}\) );  
Step 2: The sub-network table of node \(q_{v,start}\) is determined as \(G_{start}^{\prime\prime}\), where \(G^{\prime\prime}\in\{G_{w},G_{w^{\prime}}\}\) determines that the sub-network of node \(q_{v,end}\) is \(G_{end}^{\prime\prime}\), and the communication interaction between the sub-networks is marked as \(I_{(G_{w^{\prime},end}^{\prime\prime})}(t)\). The optimal path within the sub-network can be obtained by looking up the table;  
Step 3: A search for sub-networks \(G_{start}^{\prime\prime}\) and \(G_{end}^{\prime\prime}\) within time \(t_{valid}\subseteq[t_{start},t_{end}]\) is conducted based on node orbit/path prediction results, and a set of sub-networks that can be linked is established. A search for each sub-network in the obtained set of sub-networks is carried out again for the set of sub-networks that can be linked within time \(t_{valid}\in[t_{start},t_{end}]\), and the two search results are merged until no new sub-networks are added. At this point, the set of sub-networks that can be linked within the marked task cycle is \(\bar{G}_{mid}^{\prime\prime}=\{G_{mid\_0}^{\prime\prime},G_{mid\_1}^{\prime \prime},\cdots,G_{mid\_V-1}^{\prime\prime}\}\), so the set of valid linked sub-networks\(\vec{G}^{\prime\prime}_{valid}=\{G^{\prime\prime}_{start},\vec{G}^{\prime\prime}_{ mid},G^{\prime\prime}_{end}\}\subseteq\vec{G}^{\prime\prime}_{i}\) within a single task corresponds to the effective search time \(t_{valid}\subseteq[t_{start},\,\overline{t}_{mid},t_{end}]\);  
Step 4: A set of related routing sequences is randomly selected, that is, the routing sequence \(\stackrel{{\rightarrow}}{{I}}(\vec{C}^{\prime\prime}_{k(u),G^{ \prime\prime}_{j(u)}})(t)\) satisfies \(k(u),j(u)\in\{start,mid\_0,mid\_1,\cdots,mid\_V-1,end\}\), and number of hops \(u\leq\Phi_{\max}\) and \(G^{\prime\prime}_{j(u-1)}=G^{\prime\prime}_{k(u)}\), \(G^{\prime\prime}_{k(0)}=G^{\prime\prime}_{start}\), \(G^{\prime\prime}_{j(V-1)}=G^{\prime\prime}_{end}\).  
Step 5: The maximum routing delay that must meet the following is defined  
\[\sum_{U}\sum_{G^{\prime\prime}}\sum_{t^{\prime\prime}}Data(q_{\psi},q_{v}{}^{ \prime},t_{mid\_v})/f(q_{\psi},q_{v},q_{\psi}{}^{\prime},q_{v}{}^{\prime},t^{ \prime\prime})\leq\Delta_{\max} \tag{4}\]  
where \(Data(q_{\psi},q_{v}{}^{\prime},t_{mid\_v})\) represents the amount of data that needs to be transmitted in time window \(t_{mid\_v}\) for load \(q_{v}\) at node \(q_{\psi}\), and \(t^{\prime\prime}\in[t_{old\_s},t_{old\_s}]\), \(t_{old\_e}\leq t_{mid\_v^{2}}\) if it does not meet the requirements, the process returns to step 4.