## 1 Introduction  
Although the CPU of mobile devices is constantly being updated and iterated, and their computational capabilities are gradually improving, the processing power of mobile devices still appears to be insufficient, especially when compared to the explosive growth of data. This is due to limitations such as battery capacity and computational resources. With the continuous development of the Internet of Things (IoT) and communication technologies, there are an increasing number of computationally intensive and latency-sensitive applications, like image processing and machine learning, or those requiring real-time processing, such as augmented reality (AR) and autonomous driving, which are particularly challenging for mobile devices to handle [1, 2]. Although cloud servers have powerful processing capabilities, running resource-intensive applications requires significant time for data transmission, resulting in unpredictable communication delays [3, 4, 5]. The emergence of mobile edge computing (MEC) addresses the shortcomings of both cloud and mobile devices, offering great potential in solving the task offloading problem [6, 7, 8, 9, 10]. Although [11, 12, 13, 14] propose new computational models in MEC, it still faces numerous challenges. Taking object and pose recognition as an example, a typical object and pose recognition application requires several steps: feature extraction, object model matching,pose estimation, clustering, and classification [15]. When devising offloading strategies for these tasks, there are two factors that we need to consider. The first factor is whether the device has cached the necessary services for task execution. This is one of the key issues in the development of future 6G technology [16; 17]. Service caching not only enhances network reliability, adaptability, and bandwidth utilization, but also, by caching the required services on the execution node, effectively supports offloading strategies, thereby improving the performance of the algorithm [18]. However, most research on service caching focuses on the issue of service placement [2; 19; 20], which incurs higher costs and time compared to task transmission and execution [20]. For instance, a machine learning model requires a large amount of data for training, and if we wanted to migrate this service to another execution node, it would take a considerable amount of time. This is not desirable for delay-sensitive applications. Therefore, like in [10], we assume that the service is already placed on the execution node. We focus on the impact of service caching on the offloading strategy. The second factor is whether there is dependency among tasks. For instance, the pose estimation task can only be executed after the object model matching task. Each subtask requires the result of its parent task to continue execution, and different offloading strategies directly affect real-time performance. Traditional coarse-grained scheduling only considers operations at the application level [21], which makes it unable to address the complex and diverse demands of current applications. Although most current studies take this into account, they either rank subtasks based on delay constraints and execute each subtask sequentially [22; 23; 24; 25], or use heuristic algorithms to solve such problems [26; 27; 28; 29]. This results in certain limitations and makes it difficult to ensure performance guarantees. Therefore, service caching and task dependency both impact the performance and feasibility of offloading strategies. When considering task offloading, if service caching is considered without considering the dependency between tasks, the offloading strategy may fail to execute [10]. Conversely, if only task dependency is considered, significant time may be spent caching services for the offloading strategy, which affects the performance of the algorithm. Meanwhile, both service caching and task dependency significantly influence the integration of MEC and future 6G technologies.