## 2 Related Work  
The problem of computation offloading has been studied in recent years and many heuristic algorithms have been proposed. Several survey articles comprehensively reviewed this problem [2; 12; 13]. Fine-grain resource allocation and scheduling for multiple tasks received much attention. Several studies [14; 15; 16] investigated the problem of binary task offloading, where each task is executed as a whole either locally at the mobile device or offloaded to the MEC server. [PERSON] et al. [17] proposed a response-time-improved offloading algorithm to make offloading decision with fewer characteristics of continuous uncertain applications. [PERSON] et al. [18] presented a load-balancing approach for task offloading in vehicular edge computing networks with fiber-wireless enhancement. [PERSON] et al. [15] showed how the optimal resource allocation involves a joint allocation of radio and computation resources via a fully cross-layer approach. [PERSON] et al. in [14], proposed to minimize energy consumption for executing tasks with soft deadlines. Under the Gilbert-Elliot channel model, they presented optimal data-transmission scheduling by dynamic programming (DP) techniques. This work is extended in [16], where both the local computation and offloading are powered by wireless energy provisioning. Another work [19] formulated a non-cooperative game and presented a fairness-oriented computation offloading algorithm for cloud-assisted edge computing. In practice, many mobile applications are composed of multiple procedures/components, making it possible to implement fine-grained (partial) computation offloading. Accordingly, partial offloading schemes have been proposed to further optimize MEC performance [8; 9; 10; 11; 20]. [PERSON] et al. [8] investigated an energy-efficient task-graph-offloading problem for multicore mobile devices. They designed a critical-path-based heuristic which recursively checks the tasks and moves tasks to the correct CPU cores to save energy. [PERSON] et al. [9] proposed an heuristic algorithm to minimize the overall application execution cost under task deadlines. Nevertheless, these studies involve list-scheduling-based constructive heuristics, thereby suffering from poor performance due to unfavorable schedules which may cause unnecessary processor waiting times. Further, [PERSON] et al. [10] proposed a polynomial time-approximation algorithm to optimize the makespan under energy budgets for offloading (tree-shape) task graphs on edge devices. However, Ref. [10] relies on an unrealistic assumption that the mobile devices are assumed to possess infinite capacity, i.e., the devices can simultaneously process an infinite number of tasks without reduction in the processing speed for each task. Another work [20] formulated the task-graph-offloading problem via integer linear programming, but no novel solution was presented. Both the binary offloading and partial offloading strategies investigate resource allocation for a given set of tasks submitted by a single user. For multiuser systems, a number of studies on joint radio- and computational-resource allocation has also been proposed [21; 22; 23; 24; 25; 26; 27]. [PERSON] et al. presented an opportunistic task-scheduling algorithm over co-located clouds in mobile multiuser environments. In [23], the authors considered the multiuser video compression offloading in MEC and minimized the latency in local compression, edge cloud compression and partial compression offloading scenarios. [PERSON] et al. [26] studied a device-to-device (D2D)-enabled multiuser MEC system, in which a local user offloads their computation tasks to multiple helpers for cooperative computation. [PERSON] et al. [27] proposed a mobility-aware offloading algorithm for multiuser mobile edge computing. These papers studied the assignment of finite radio-and-computational resources on a server among multiple mobile users to achieve system-lever objectives. [PERSON] et al.