the relays. In[@NOM], a reactive relay selection policy is proposed. More specifically, instead of considering only the [*SR*]{} and [*RD*]{} channel gains, the feasibility of IC is also examined. In this way, with a very simple IC condition the following two cases for relay selection are given.

-   If candidate relay $R_k$ can perform IC then it may be selected to receive from the source based on the following value: $$\begin{aligned}
    R^*=\arg\max_{R_k\in \mathcal{C}} \min \{ g_{S,R_k} , g_{R_k,D}   \}.\end{aligned}$$

-   On the other hand, if $R_k$ cannot perform IC then it can be selected after competing with the rest of the relays as below: $$\begin{aligned}
    R^*=\arg\max_{R_k\in \mathcal{C}} \min \left\{ \frac{g_{S,R_k}} {g_{R_t,R_k}} , g_{R_k,D}   \right\}.\end{aligned}$$

It is obvious that by having two simultaneous transmissions by the source and the transmitting relay reduces the diversity of the network as $R^*$ can not participate in the selection process due to the half-duplex constraint. On the other hand, if IRI is effectively mitigated, a full-duplex behavior can be achieved and the half-duplex loss is leveraged.

$\max-\max$ relay selection (bound)
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The $\max-\max$ relay selection [@IKH2] is the first policy that exploits buffering capability at the relay nodes and is used as a reference selection 