### Related Work
Then, a relay is selected using an optimal stopping approach. The proposed scheme significantly reduces the time taken for probing of devices before selection of a relay. Similarly, [PERSON] et al. [7] proposed a decode and forward relaying for a cooperative D2D communications. The relay has a transmission power proportional to the social trust that is, the relay transmits at a high power when it has strong social relationship with the source. They used optimal stopping approach while probing socially trusted nodes sequentially to select a relay. This helps to maintain the balance between relay probing cost and performance gain. The major setback of their research is that the comparison of the proposed scheme is done with generic schemes (direct communication and random relay selection). Uniform distribution is used to assume the social trust among users, which is less realistic. Additionally, they analyzed the scheme only for a specific distance (100 m) between source and destination. However, in reality, source-destination distance can vary over time. [PERSON] and [PERSON] [12] proposed a Hybrid Relay Selection (HRS) scheme in which social information of users are utilized for selection of a relay. We compare the performance of HRS scheme with relay selection schemes proposed in this paper. In HRS, mobile devices that have a strong relationship with each other are assumed to have high value of social trust between them. Such devices having strong social trust with a source can potentially relay data with high transmission power. Both link characteristics and social trust between users are considered for relay selection. HRS selects a relay around the source. To select a relay, a source probes devices that are not engaged in communication and located within a circular region with the source at the center. Only those devices which have social trust greater than a threshold value are probed. HRS assumes the transmission power of a relay is linearly proportional to the social trust between the source and the relay. The social trust between the users in the network is modelled using Pareto distribution. The source calculates the data rate offered by each of the probed nodes and chooses the node that offers maximum data rate as a relay. The authors show that the average throughput of HRS is higher than two other schemes: Distance-based Relay Selection (DRS) and Social-based Relay Selection (SRS). They also suggested that the relay selection region should neither be too small nor too large. The major downside of HRS is that the throughput is low for small search radius due to frequent selection of long distance links. Also, the throughput is low for large search radius. This is because of the significant time duration spent for probing. Furthermore, the performance of HRS is not compared against relay selection schemes proposed by other researchers. Our previous work [9] proposed a midpoint relay selection scheme that selects a socially trusted device located around the midpoint of the distance between the source and the destination. The scheme performs better than HRS. The drawback of the scheme is that it probes all the devices within the circular region having social trust above a threshold value. We overcame the limitation by proposing two relay selection schemes Midpoint Relay Selection Scheme using Social Trust and Midpoint Relay Selection Using Social Distance in Reference [10]. In Reference [11], we proposed a midpoint relay selection scheme that improves the throughput of D2D communications even when social trust among the users are strong, provided that the BS can accurately estimate social trust information of users. Different from all the papers above, this paper proposes midpoint relay selection schemes that incorporates battery power of devices together with social trust information of users to select a relay with the aim to maximize average throughput of D2D communications.