In this paper, we study the problem of resource allocation in SC-FDMA systems. A sum-utility maximization is considered where the utility of each user may be neither additive nor super additive. Unlike OFDMA, in addition to the restriction of allocating a subchannel to at most one user, the multiple subchannels allocated to a user in SC-FDMA must be consecutive. This makes the resource allocation problem prohibitively difficult and challenging. We provide a fundamental complexity analysis of the optimization problem for general non-additive utility functions and show that not only the problem is NP-hard but also approximating it within a factor better than $ {{2011}over {2012}}$ is not possible unless ${rm P}={rm NP}$. An efficient cutting plane algorithm is presented and five suboptimal heuristics are also presented that achieve near optimal solution in different scenarios. Computational results of the cutting plane and heuristic algorithms are reported and a comparison between these heuristics is provided as well.