Abstract
The Gamma network is a multiprocessor interconnection network with redundant paths between source and destination terminals. The basic switching element in this network is a 3 × 3 crossbar, and the stages are linked by “power of two” and identity connections. The Gamma network is known to realize many classes of permutations useful in parallel processing, and in this paper a detailed study of various classes of permutations passable by the network with a simple control algorithm is presented. Conditions for passability of an arbitrary permutation with this algorithm have been formulated and used to show that several useful classes of permutations in parallel processing can be realized. Although the algorithm does not utilize the full connection capability of the network, it produces conflict-free routing for most of the useful classes of permutations the network is capable of passing.
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