A self-routing permutation network

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A self-routing permutation network is a connector which can set its own switches to realize any one-to-one mapping of its inputs onto its outputs. Many permutation networks have been reported in the literature, but none with the self-routing property, except crossbars and cellular permutation arrays which have excessive cost. This paper describes a self-routing permutation network which has O(log3n) bit-level delay and uses O(n log3n) bit-level hardware, where n is the number of inputs to the network. The network is derived from a complementary Beneš network by replacing each of its two switches in its first stage by what is called a 1-sorter and recursively defining the switches in the third stage as self-routing networks. The use of 1-sorters results in substantial reduction in both propagation delay and hardware cost when contrasted with O(n) delay and O(n1.59) hardware of the recursively decomposed version of a complementary Beneš network. Furthermore, these complexities match the propagation delay and hardware cost of Batcher's sorters (the only networks, other than crossbars and cellular permutation arrays, which are known to behave like self-routing permutation networks). More specifically, it is shown that the network of this paper uses about half of the hardware with about four-thirds of the delay of a Batcher's sorter. © 1990.

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Journal of Parallel and Distributed Computing

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