Since Tassiulas and Ephremides proposed the maximum weight scheduling algorithm of throughput-optimality for constrained queueing networks in 1992, extensive research efforts have been made for resolving its high complexity issue under various directions. In this paper, we resolve this issue by developing a generic framework for designing throughput- optimal and low-complexity scheduling algorithms. Under the framework, an algorithm updates current schedules via an interaction with a given oracle system that generates a solution of a certain discrete optimization problem in a fi-nite number of interactive queries. The complexity of the resulting algorithm is decided by the number of operations required for an oracle processing a single query, which is typi- cally very small. Somewhat surprisingly, we prove that an al- gorithm using any such oracle is throughput-optimal for gen- eral constrained queueing network models that arise in the context of emerging large-scale communication networks.To our best knowledge, our result is the first that establishes a rigorous connection between iterative optimization methods and low-complexity scheduling algorithms, which we believe provides various future directions and new insights in both areas.