This paper investigates the resource allocation in terms of sub carrier assignment for maximizing the overall network throughput. In the existing subcarrier assignment algorithm, some users may obtain none of subcarrier while a few number of users with better channels obtain most of the resources. Therefore, we present an algorithm to solve the relay selection and resource assignment with the threshold constraint for relay based femtocell network. Since the time complexity of the optimal algorithm takes too much time to execute, we propose a heuristic algorithm to greatly reduce the time complexity while the achieved throughput is close to the optimal case. Simulation results show that our proposed method can largely save the execution times with only slight difference of throughput compared to the optimal case. By using the proposed heuristic algorithm, we greatly reduce the execution time and maintain high system performance for the resource assignment.