## 1 Introduction  
With the development of networks and the popularization of user devices (UEs), people can easily access networks and obtain desired services. However, the number of service requests generated per moment increases significantly. Moreover, more and more delay-sensitive and computation-intensive applications, such as autonomous driving, virtual reality, augmented reality, cloud robotics, and remote surgery, etc. [1] have been integrated into people's daily life. UE's computing capabilities are limited, so they cannot complete the tasks of these applications on their own within low delay [2]. High task completion delay will affect the quality of user experience seriously. Cloud servers have strong computing capabilities. However, they are deployed at the core network layer and are too far away from UEs. Therefore, transmitting tasks to cloud servers for computing will bring extremely high delay and extra transmission energy consumption [3]. Mobile edge computing (MEC) proposed by the European Telecommunication Standardization Organization (ETSI) has attracted people's attention. It makes the information technology (IT) service environment and cloud computing capacity sink from the cloud to the wireless access network, enforces the computing capacity to the edge of mobile networks, and reduces the response delay effectively [4]. Users can offload tasks to nearby network edges for computing via terrestrial networks, e.g., cellular networks [5]. To implement MEC in cellular networks, an MEC server with computing capability is deployed at a base station (BS). The BS can receive tasks offloaded by UEs within its coverage area and use its MEC server to compute tasks [6]. This not only makes up for UEs' computing capabilities, prolongs their battery life, but also achieves better service [7]. Terrestrial networks cover only about 20% of the earth's land area, and less than 6% of its surface [8]. Satellite networks can complement and expand terrestrial networks, so as to achieve seamless global coverage, e.g., low earth orbit (LEO) satellite networks can provide users with all-weather stable and reliable services in both densely populated areas and rural areas [9]. In order to expand the service scope and provide reliable and on-demand services, etc., the convergence of satellite networks and terrestrial networks, i.e., satellite-terrestrial networks (STNs) has become a research hotspot [10]. STN has advantages, e.g., wide coverage, strong robustness, etc. This paper introduces MEC into STN, i.e., the study is carried out in MEC-enabled STN. For the areas that are not covered by terrestrial networks, users can rely on satellite networks to obtain services. Comparing with terrestrial networks, LEO satellite networks can provide high-capacity backhaul, large coverage, and more flexible network access services [11]. In addition, LEO satellite networks have advantages, e.g., low transmission loss and low transmission delay, which can ensure UEs' quality of service (QoS) [12]. MEC servers can be deployed at LEO satellites, so users can obtain MEC services by communicating with LEO satellites [13]. UEs can offload tasks to LEO satellites for computing. Comparing with sending tasks to the remote cloud, the delay is improved significantly [14]. It should be noted that there is symmetry between satellite networks and terrestrial networks, but there is asymmetry between their resources. Comparing with MEC servers of BSs, MEC servers of LEO satellites have fewer computing resources. When overmany UEs request tasks simultaneously or overmany computing resources are required, LEO satellites' MEC servers may not provide sufficient computing resources for all UEs [15]. The ideal gain cannot be obtained only by offloading tasks to LEO satellites for computing. This situation highlights the necessity of satellite-terrestrial cooperation. LEO satellites migrate some tasks to BSs in adjacent areas, utilizing computing resources of the BSs' MEC servers to compute tasks.