## 2 Related Works and Technology  
Numerous works have been devoted to D2D communications from different perspectives. [PERSON] and [PERSON] [9] address issues, solutions, and challenges in D2D communication in 5G environments. [PERSON] et al. [10] provide a comprehensive survey on D2D communication, featuring basic concepts, target applications, potential challenges, and future directions. Among other issues, routing in D2D networks has received considerable attention due to its important role in system performance. In [11], [PERSON] and [PERSON] present an excellent review of recent advances in D2D routing technology. They classify use cases into three classes: multi-hop D2D routing, multi-hop D2I/I2D routing, and ad hoc routing. Focusing on multi-hop D2D routing, our work differs from others in that we formulate the overall route planning problem as an NP-hard optimization problem and approach the real-time routing problem using an integrated bidirectional and lifelong-planning A* algorithm. Our approach furnishes valuable insight into the D2D routing problem and develops a method from a new perspective by incorporating classical wisdom. Studies [12; 13; 14] show that group communication has become a common form of mobile networking. Mobile users in proximity form a communication group partaking in the same interest in some digital content. Once a user has downloaded a particular content, the other users can download the content from the user via D2D group communication without the need for cellular communication. These observations imply that an efficient D2D group communication scheme, as the focus of this study, is essential for future mobile networking. A number of works contributed to D2D group communication. An early work [15] analyzes the performance difference between multi-hop and single-hop transmission. However, the path selection problem was not properly addressed. In [16], message forwarding is completed by broadcasting. By doing so, the number of control messages can be significantly reduced. However, it can also introduce a broadcast storm problem. Our approach adopts a unicast scheme. We define the cost for individual transmission links and then find a path with the least cost. In [17], a UE with less interference is selected as the relay UE. The approach may not have the optimal outcome, since the systemic relationship among the sender, relay, and receiver is not accounted for. The study in [18] takes into consideration the location of UEs. The coverage of a base station is partitioned into five regions. The region close to the base station is excluded from the selection due to severe interference. Their approach prefers a relay located in the same region a sender resides in. Both [17; 18] had achieved their objectives. Nevertheless, both schemes did not consider that a single-hop relay may fail to fulfill the forwarding need, so a multiple-hop relay is required to complete the forwarding. A multi-hop relay path is needed to accomplish the transmission task. Finding a relaying path (a route) with less cost for D2D group communication is the core issue of D2D communication [19; 20; 21]. To facilitate multi-hop D2D communications in 5G networks, a framework for virtual mesh networking is created in [19]. Base stations gather terminal link and topology data before creating a virtual mesh network among the terminals in accordance. The virtual mesh routing method, which also considers terminal mobility and connection failure, then chooses the routing path for end-to-end communications. In order to provide D2D content sharing with multi-hop communication capabilities, [PERSON] et al. [20] suggest a game theoretic strategy. The routing and price graphs are produced by modeling a Nash bargaining game with a subset of players, where a novel incentive mechanism is used to encourage cooperation. [PERSON] modifies the standard DSR (Dynamic Source Routing) protocol in [21] to allow for quick routing decisions.