This paper addresses a constrained resource allocation problem in Cloud Radio Access Networks (C-RAN). This problem consists in determining the best strategies to assign antennas (Remote Radio Head - RRH) demands to available edge data centers (pool of BaseBand Units - BBU) when jointly optimizing communication latency and resource consumption. Telecommunications Service Providers (TSPs) need new algorithms that enable to jointly reduce their OPEX and CAPEX when embracing C-RAN technology. This paper proposes a mathematical model based on an integer linear programming formulation, to optimally solve the constrained resource allocation problem. To scale and handle much larger number of antennas and edge data centers in acceptable times, a faster and more efficient algorithm based on matroid theory is provided. Simulation results show the scalability of our algorithms and quantify the potential benefits of the discussed approaches in the context of C-RAN.