## 1 Introduction
The instability of the ISL can easily disrupt the regularity and predictability of the LEO constellation when a satellite or link fails [10]. This is because an unconnected ISL can cause the actual LEO constellation to differ from the predicted LEO constellation. The hop-by-hop routing scheme relies only on the geographical information of the LEO constellation. Because the hop-by-hop routing scheme calculates the shortest routing path within a given topology, it cannot detect link failures caused by ISL instability. A hop-by-hop routing scheme requires a method for sharing link-failure information to resolve unpredictable topological differences. Conventional flooding methods result in high communication overhead and require a more efficient information-sharing approach. Flooding broadcasts the link state throughout the entire network, similar to the \(n\)-hop flooding approach presented in [11]; \(n\)-hop flooding reduces the communication overhead by simply limiting the flooding range. Flooding-based link information exchange incurs unnecessary and redundant link failure information. Link failure information propagated to an unspecified number of nodes within the network generates communication overhead. Wasting a limited onboard processing power of LEO satellites can reduce the resources needed for satellite operation and disrupt reliable end-to-end transmission. The routing path has to be created according to the changing topology while minimizing the link information messages exchanged due to frequent topology changes. Considering the limited processing power of satellites, a routing technique that minimizes link information messages for creating a routing path is needed. In this paper, we propose a distributed detour routing scheme to minimize overhead. When a link failure occurs in LEO satellite networks, the link failure information should be shared with as many nodes as possible, consuming the least amount of link resources. The proposed scheme finds the best detour point with minimal communication overhead by combining a rapid detour with selective flooding. A preliminary detour path is created using rapid detour packets transmitted through a failed link without any communication overhead. Communication overhead is minimized by selectively flooding the starting point of the generated preliminary detour path to the best detour point within the minimum hop region (MHR) of the packet. The path flooded to the best detour point is combined with the detour path created by the rapid detour to create a pre-detour path. Link-state packets are also exchanged for exclusive link failures to detect link recovery and effectively switch to the original path. This combined distributed detour routing scheme can achieve low delay and packet drop rates with minimal communication overhead. The main contributions of this study are as follows:  
* Rapid detour routing is proposed for a packet encountering a link failure in LEO satellite networks. Rapid detour routing instantaneously detours the failed link and maintains the shortest path without the need for additional path calculation or link-state exchange when a link failure is encountered. * A selective flooding algorithm is proposed to minimize overhead. The selective flooding utilizes MHR to identify the best detour points without additional hops. * A link recovery procedure is defined to switch the detour path to the original path. By creating a detour path utilizing rapid detour routing and selective flooding, we can switch back to the original path and minimize end-to-end delay. The remainder of this paper is organized as follows. In Section 2, related studies are introduced. Section 3 presents the system model of the proposed scheme. In Section 4, the distributed detour routing and recovery schemes are presented. In Section 5, the simulation results are presented. Finally, conclusions are drawn in Section 6.