## 4 Proposed Routing Scheme
### Distributed Detour Routing Scheme
After detecting a link failure, similar to the link-state algorithm, the node floods the information to all other nodes in the network for the routing table convergence. When a recovered link is detected, the entire network is flooded with the same process used during link failure to refresh the routing table. * Disruption tolerant distributed routing (DTDR) [11]: In this scheme, the node that detects a link failure utilizes an \(n\)-hop flooding strategy, where flooding is restricted to a defined area. Nodes that receive the \(n\)-hop flooding update their alternative routing tables based on the link failure information. The alternative routing table prioritizes using the secondary direction over the primary direction for paths leading to the destination of the detour link failures. In the simulation, we adopted the three-hop flooding technique proposed in the referenced paper. ### Communication Overhead from Flooding Comparison

In this simulation, we compared the communication overhead incurred when sharing link failure information with other nodes following link failure. Specifically, we considered only messages that shared routing information, excluding data transmission. The number of communication overheads is given by Equation (4). In this paper, since the number of flooding messages is equivalent to the communication overhead, the number of flooding messages is calculated as follows:

\[\sum_{i=0}^{N}M_{i}, \tag{7}\]

where \(M_{i}\) denotes the number of flooding messages generated at each stage, and the range of flooding is \(N\). In this experiment, the \(n\)-hop flooding in DTDR initially propagates three messages, i.e., \(M_{0}=3\), and since the flooding range is three, \(N=3\). From the subsequent steps, the flooding starts from the node that received the message in the previous step, i.e., \(M_{i}=3\times M_{i-1}\). Conversely, the proposed selective flooding uses a flooding range that extends from the rapid detour point to the detour point in terms of hop count. Since only a single link is used for flooding at each hop, \(M_{0}=1\) and \(M_{i}=1\) throughout. The transmit power used to send flooding messages consumes onboard power in proportion to the number of messages. The onboard power of each satellite used for flooding is proportional to the number of transmitted messages. In other words, typical flooding consumes the transmit power for three links, excluding the link that received the message. Figure 7 shows the communication overhead from flooding based on the link failure rate. OPSPF results in the highest communication overhead. This is because the flooding of the entire network is proportional to the number of ISLs connected to the LEO satellite network. As a result, a single link-state change causes a huge communication overhead. DTDR utilizes the \(n\)-hop flooding technique, which limits flooding to a restricted area. Since three-hop flooding was used in this experiment, all nodes located within three hops are flooded based on the node that detected link failure. However, it still generates duplicate flooding messages for an unspecified number of nodes. The proposed scheme outperforms both OPSPF and DTDR. This is because the proposed scheme searches for the optimal detour point within a predefined MHR that intersects the paths of the packets. Subsequently, the proposed scheme only communicates link failure information to the nodes at the detour point and along the selective flooding path. This approach eliminates redundant and unnecessary information exchanges, resulting in a significant reduction in

communication overhead. The \(n\)-hop flooding consistently floods link-state information whenever a packet encounters a link failure. The proposed scheme, however, demonstrates a significant reduction in the number of overheads by either not performing selective flooding or by flooding less than the number of routing hops, depending on the location of the link failure.