Software-Defined radio (SDR) is a future-proof solution for designing flexible and adaptable wireless networks and equipments. It replaces conventional radio hardware with reconfigurable, reprogrammable radios. A graphical approach for designing flexible SDR multi-standard systems is proposed, which provides all the possible alternatives of implementation capable of realizing the multi-standard design. However, a cost function which evaluates the cost of any one of these options is proposed in previous work. All these ideas are briefly mentioned in this paper but however, our goal is to help finding the option of implementation which has the minimum cost. Graph theory is adopted and particularly the study of directed hypergraphs, to present a new idea algorithm capable of solving this optimization problem. This algorithm provides an exact-optimal solution, unlike the previously applied heuristic methods which give a near-optimal solution. Furthermore in this work, we analyze the computational complexity of our algorithm.