## 1 Introduction  
The low Earth orbit (LEO) satellite network can provide global communication services across the Earth through multi-hop routing using inter-satellite links (ISLs). In rural, mountainous, and marine regions where maintenance of the terrestrial network infrastructure is difficult, the LEO satellite network can provide communication services with global coverage through ISL without ground gateway relays. For example, Iridium is a network consisting of 66 LEO satellites, providing a data service with global coverage [1]. SpaceX has recently announced a plan to deploy 12,000 LEO satellites over the next 20 years for global coverage [2]. Therefore, the LEO satellite network can provide global coverage with relatively low latency and is an important part of the next-generation network in providing seamless global coverage [3]. A routing algorithm that considers the characteristics of LEO satellites is necessary to provide global communication services in the LEO satellite network. LEO satellites have mobility, but the ground station is fixed on the ground. The location of the ground station can be a factor in determining the routing path [4]. Data transmission in inter-satellitecommunication requires pointing, acquisition, and tracking (PAT) processes to establish ISL connections [5]. The ISL connectivity is unstable during the PAT process because of satellite mobility and varying orbital characteristics [6]. Given the instability of ISL, in the absence of a connected link, the satellite may assume a link already exists. This may lead to frequent differences between the actual and the routing topologies. Continuous data transmission over a nonexistent link can cause packet drop and communication interruptions. Frequent topological differences may eventually collapse network reliability. Therefore, topological differences should be considered in designing routing algorithms for LEO satellite networks. To address the topology differences in LEO satellites, link-state routing has been proposed [7]. In link-state routing, satellites periodically share link-state information with adjacent satellites and flood any changes in the link state throughout the network. Flooding is a method of broadcasting this information to the network when a change occurs in the network topology. Link-state routing allows real-time monitoring of the link state, enabling the immediate handling of topology differences. However, the instability of ISLs intensifies topological differences, leading to frequent flooding, which imposes massive communication overhead on all the ISLs within the network. In particular, LEO satellites have extremely limited processing power and storage because of space and technological constraints [8]. Minimizing the communication overhead of the exchange link state is crucial for the onboard constraints of LEO satellites. To cope with the communication overhead from routing topology maintenance, a hop-by-hop routing scheme was proposed [9]. In this scheme, satellites calculate the routing table independently and only use the next hop for forwarding. The movement of LEO satellites is predictable, as they move at a constant speed along a predefined orbit. This allows determining the next hop without the need for sharing the link state because the position of the satellite can be determined at any given moment. In a given topology, the optimal next hop can be selected without exchanging information to reach the destination. For example, as the inter-ISL length decreases at high latitudes, the inter-ISL should be selected in the routing path and the intra-ISL is used for transmission at high latitudes because intra-ISL always has the same length, thereby obtaining the shortest inter-ISL in the entire routing path. A hop-by-hop routing scheme is performed without link-state exchange using only the geographic information of the LEO satellite through the LEO constellation information. Therefore, the communication overhead is reduced because there is no need for link-state exchange for route convergence.