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Abstract: A distributor is a time-multiplexed switch that sorts input signals to output ports in the round-robin fashion. We present an efficient construction of distributors for all in the form of parallel distributed-control networks, where the maximum size of a building block is the largest prime factor of . The construction achieves the lowest known complexity for distributors of all sizes within the practical range. Meanwhile, we also offer an algorithm for the adaptation of a larger distributor into a smaller distributor. The adaptation is useful when the size contains large prime factors. Rigorous algebraic formulation throughout the paper keeps the algorithmic construction transparent and affords many variations for the flexibility in implementation. [Copyright &y& Elsevier]