## 3 Related Work  
Multihop D2D communications in LTE-A networks have been studied in several works, e.g., [12; 13; 14; 15; 16; 17]. In [12], authors consider multihop D2D communications in order to extend the network coverage and propose a resource allocation strategy to optimize the throughput along the multihop paths. The study is restricted to two-hop communications where one UE is identified as relay node for one pair of transmitting and receiving UE, where each hop is a unicast point-to-point (P2P) D2D transmission. The work in [13] proposes a theoretical formulation for computing the outage probability of multihop communications. Also in this case, P2P D2D transmissions are considered. An opportunistic multihop networking scheme for Machine-type Communications is presented in [14]. UEs exploits the Routing for Low-power and Lossy Networks (RPL) algorithm used in Wireless Sensor Networks (WSNs) to compute the best route toward a given destination. In [15], game theory is applied to find the best multihop path for uploading content from one UE to the eNB. Both [14; 15] differ from our work as they deal with the problem of delivering messages toward a given destination, instead of disseminating them to all the UEs within a given target area. Moreover, P2 MP communications are not considered. In [16], P2P D2D communications are considered in order to enhance the evolved Multimedia Broadcast and Multicast Services (eMBMS) provided by LTE-A networks. In this case, the eNB transmits its multimedia content to a subset of UEs and the latter exploit D2D links to forward the data to UEs with poor channel conditions in the downlink, i.e., cell-edge UEs. A similar problem is tackled in [17], where UEs receiving data from the eNB use one P2 MP D2D transmissions to distribute the data to neighboring UEs. The above paper focuses on finding the best subset of relay UEs so that  
Figure 2: **(a)** Scheduled Resource Allocation (SRA); **(b)** Autonomous Resource Selection (ARS). \(\Delta\) is the time between the generation of new data and the actual transmission. UE: User Equipment; eNB: eNodeB; RAC: Random ACCess; BSR: Buffer Status Report; TTI: Transmission Time Interval; TX: transmission. the total power consumption is minimized and the rate requirements for all the UEs are satisfied. None of the above works address the problem of disseminating UE-generated contents toward all UEs within a geographical neighborhood. Centralized resource scheduling is sometimes assumed in Wireless Mesh Networks (WMNs), although far less often than distributed resource scheduling, (see, e.g., [19; 20]). In this context, our broadcasting problem is superficially similar to the one of channel assignment and/or link scheduling in WMNs. However, the assumptions are quite different from those made in LTE-A, since nodes in a WMN are usually equipped with few radios, which can be tuned to a larger number of channels. In LTE-A, all UEs have as many \"radios\" and \"channels\" as the number of RBs, which is in the order of several tens. More importantly, RBs can be allocated dynamically to UEs, whereas the algorithms presented in the literature often assume periodic transmissions and long-term, semi-static resource allocations. Moreover, unicast P2P transmissions are considered. For these reasons, the broadcasting problem considered in this paper cannot be accommodated using the above algorithms. Broadcast diffusion problems have been addressed in the context of mobile ad-hoc networks (MANETs) (e.g., [21; 22]), especially to support the dissemination of routing alerts or for gossiping applications [23]. Unlike LTE-A, where resources are centrally scheduled by the eNB on demand, the above networks are infrastructureless and have distributed resource allocation. Work [24] reviews and classifies the broadcasting methods in MANETs, focusing on how they try to limit collisions, the latter being the key issue in an infrastructureless network.