in a two-way relay network and investigates an opportunistic scheduling that maximizes the system sum-rate while ensuring buffer stability.

In the majority of the aforementioned works the main target is outage probability reduction or throughput improvement. Another characteristic that is of utmost importance in wireless cooperative networks is energy-efficiency. The proposed algorithm in [@NOMspringer] selects the end-to-end paths based on their achievable capacities and uses hierarchical and adaptive modulation. In this way the power of the source and the transmitting relay are adjusted according to the level required for successful reception. In various works (see, e.g., [@FENG; @ZHOU; @CHEN; @SHENG] and references therein) relays are assumed to be battery operated. Due to this practical assumption, the proposed algorithms select the best relays according to two factors. First, the selected relay will spend the minimum amount of energy that is required to surpass the outage threshold of the network. Second, by considering the remaining energy of each node, relays that were selected often will be protected in order to extend their operation and increase the network lifetime. A variation of this energy-efficiency metric is provided in [@AMIN], where circuit-energy consumption is considered and dynamic time allocation is implemented. Also in [@MOUS], 