This paper considers a dynamic spectrum allocation (DSA) for efficient distribution of the spectrum resource by allocating the spectrum to be responsive to demand variations. In this DSA model, a spectrum broker (SB) is responsible for the allocation of the spectrum with the regional license inside the region of responsibility and the coordination of the wireless interference inside the region for quality of service (QoS) provisioning over the allocated spectrum. In this paper, we address the interference constrained DSA problem and propose an optimal DSA scheme by applying the binary integer programming (BIP) approach to the DSA. Within the interference graph based interference constraint, the proposed scheme obtains a optimal set of binary decisions on whether to allocate or not allocate the channels to the access points within the region in accordance with the objective (i.e., maximization of the revenue of the SB, maximization of the spectrum utilization inside the region, and multi-objective optimization compromising the revenue and spectrum utilization maximization). Simulation results demonstrate that the proposed scheme efficiently distributes the spectrum resource in accordance with the corresponding objective and the multi-objective optimization obtains the compromise solution depending on the preference between the revenue and spectrum utilization.