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In this paper, we consider two relay assignment schemes for cooperative networks comprising multiple source-destination pairs. Both schemes are based on the max-min criterion and aim at achieving the maximum spatial diversity for all pairs. One scheme is used as a performance benchmark since it considers all possible relay assignment permutations and selects the best one. The other scheme, on the other hand, considers only a subset of those permutations and selects the best one. The advantages of the latter one is that it reduces the complexity of the assignment process, in addition to making the performance analysis tractable. We examine these schemes over asymmetric channels using M-ary phase shift keying signaling. We consider both amplify-and-forward (AF) and decode-and-forward (DF) relaying where we derive expressions for the end-to-end (E2E) symbol error rate (SER). In both cases, we show that the full spatial diversity is achieved. To account for error propagation in DF relaying, we adopt a threshold-based relaying scheme whereby the relays forward only bits that are deemed reliable and remain silent otherwise. We compare this scheme to Genie-aided relaying where the relays forward only correctly decoded bits. We analyze these two schemes and derive expressions for the E2E SER performance. We present several numerical examples that validate the analytical results.