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This paper considers the important problem of efficient allocation of available resources (such as radio spectrum and power) in orthogonal frequency-division multiple-access (OFDMA)-based multicast wireless systems. Taking the maximization of system throughput as the design objective, three novel efficient resource-allocation schemes with reduced computational complexity are proposed under constraints on total bandwidth and transmitted power at the base station (BS). Distinct from existing approaches in the literature, our formulation and solution methods also provide an effective and flexible means to share the available radio spectrum among multicast groups by guaranteeing minimum numbers of subcarriers to be assigned to individual groups. The first two proposed schemes are based on the separate optimization of subcarriers and power, where subcarriers are assigned with the assumption of uniform power distribution, followed by water filling of the total available transmitted power over the determined subcarrier allocation. In the third scheme, which is essentially a modified genetic algorithm (GA), each individual of the entire population represents a subcarrier assignment, whose fitness value is the system sum rate computed on the basis of the power water-filling procedure. Numerical results show that with a flexible spectrum-sharing control mechanism, the proposed designs are able to more flexibly and fairly distribute the total available bandwidth among multicast groups and, at the same time, achieve a high system throughput.