## 1 Introduction  
With the development of space technology and communication technology, the number of satellites in space has increased dramatically. In the future 6G network, satellite networks can be used as supplements to terrestrial cellular networks to achieve seamless full-domain coverage [1]. In addition, the satellite mobile system also has high viability when disasters happen [2]. When terrestrial network entities are destroyed by natural disasters, such as earthquakes and typhoons, people can rely on satellites to access services. Therefore, for remote areas that are not covered by terrestrial networks or disaster areas where terrestrial networks are destroyed, satellite networks can replace or assist terrestrial networks to provide services to users. The integration of satellite networks and terrestrial networks, i.e., satellite-terrestrial networks (STNs), has received extensive attention from the academic world and the industrial world [3]. STNs have advantages such as wide coverage, strong robustness, and strong damage resistance. Since the rise in popularity of smartphones and Internet of Things (IoT) devices, various applications have been emerging endlessly in people's daily life. Some of them,such as interactive games, face recognition, and augmented reality, require large amounts of computing resources [4]. Due to the physical size limitation and energy supply constraints, the computing capacity of devices is limited [5]. IoT devices compute tasks of these applications locally, which significantly imposes delay and reduces the quality of the experience. Mobile edge computing (MEC) provides information technology and cloud computing capabilities within the radio access networks, which are extremely close to users [6]. Edge servers are modular and miniaturized because they host cloud services that are scaled to the edge [7]. MEC servers can be deployed at multiple locations, such as base stations (BSs), access points, and satellites. Computation offloading technology makes it possible for users to utilize the computing capabilities at the edge of the network [8]. Due to MEC, the delay can be reduced and the quality of service can also be improved [9]. In this paper, we consider applying MEC technology to STNs, i.e., MEC-enabled STNs. Low earth orbit (LEO) satellite constellations can achieve seamless global coverage [10]. Moreover, LEO satellite networks have advantages of short satellite-terrestrial transmission distance and low construction cost. In addition, LEO satellite IoT can complement and extend terrestrial IoT to better achieve IoT applications, such as environmental monitoring, marine monitoring, and border control [11]. MEC servers can be deployed at LEO satellites to handle computing tasks from devices [12]. For remote areas with sparse users and insufficient terrestrial network coverage, such as mountainous areas and islands, offloading tasks to satellites is the only option. Compared to the computing resources of MEC servers deployed at BSs, the computing resources of MEC servers deployed at satellites are less due to the satellite payload constraints. Therefore, a single LEO satellite's MEC server may sometimes be insufficient to assist all IoT devices in computing tasks. For sparsely populated areas where IoT devices are widely spaced, such as deserts and oceans, inter-satellite cooperation is an effective coping approach. Sometimes, the computing workload is distributed unevenly in different space, which leads to the fact that some MEC servers may need to handle tasks more than their computing capabilities, whereas some other MEC servers still have surplus computing resources [13]. The LEO satellites launched recently are equipped with laser terminals, which can establish inter-satellite links (ISLs) with neighboring satellites [14]. For example, in the BeiDou system, ISLs can be established between two satellites if they are visible [15].