Efficient resource allocation in cellular OFDMA systems envisages the assignment of the number of subcarriers and the relative transmission format on the basis of the experimented link quality. In this way, a higher number of sub-carriers with low per-carrier bit rates should be assigned to users at cell border. This strategy has already proved its efficiency in the single-cell scenario, while no study has been provided in the multi-cell scenario with reuse factor equal to one, i.e., in presence of severe interference conditions. In this paper we propose an optimum centralized radio resource allocator for the multi-cell scenario of an OFDMA cellular system which allows to highly outperform iterative decentralized allocation strategies based on local optimization criteria. The proposed scheme is characterized by huge implementation complexity, and, hence, it can be hardly implemented in the real world. However, it can help the system designer in catching the essence of interference limi...