Cloud Radio Access Network (C-RAN) has been proposed as a promising architecture to overcome the challenges of next generation mobile networks (5G). The main concept of C-RAN is to decouple the BaseBand Units (BBU) and the Remote Radio Heads (RRH), and place the BBUs in common edge data centers (or BBU pools) for centralized processing. The optimal assignment of RRHs (or antennas) to edge data centers when jointly optimizing the fronthaul latency and resource consumption is one of the key issues in the deployment of C-RAN. This problem is NP-Hard and network operators need new assignment algorithms that can scale with large problem sizes and find good solutions in acceptable times. In this paper, we first model our constrained resource allocation problem by an exact approach based on Integer Linear Programming (ILP) formulation. Then, and for sake of scalability, we propose new heuristic algorithms with reduced complexity to rapidly achieve optimal (or near-optimal) solutions for the assignment of antennas demands to the available edge data centers. Simulation results highlight the efficiency and scalability of our proposed approximation algorithms and their ability to provide good solutions in negligible times.