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In this paper, we consider the problem of resource allocation in the DFT-Spread-OFDMA (DFT-S-OFDMA) uplink. We show that the resource allocation problem can be formulated as a set packing problem, which in general is NP-hard. We propose polynomial-time message-passing based algorithms, one of which is guaranteed to yield a solution that is within a constant fraction of the optimal solution and is also asymptotically optimal in the limit as the number of subcarriers in the system goes to infinity. The message-passing based algorithm is also extended to solve the resource allocation problem over a multi-cell uplink in a distributed fashion. Our algorithms account for finite input alphabets and non-ideal practical outer codes. Extensive simulations are performed to assess the performance of the proposed algorithms and it is shown that they yield near-optimal solutions at a low complexity and with a low memory requirement.