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An optimal cluster-based ad hoc network architecture that requires the minimum number of cluster maintenance overheads not only reduces the waste of the precious bandwidth but also saves the consumption of the limited battery power. Mathematical analyses show that the cluster maintenance overheads can be minimized by minimizing the number of generated clusters and the variance of the number of cluster members. By using the modified Quine-McCluskey (MQM) algorithm, the number of generated clusters and the variance of the number of cluster members of the generated cluster-based network architecture are minimized. Thus, the number of overheads required to maintain the cluster architecture is minimized and the precious bandwidth and the limited battery power are saved.