Abstract
The cylindrical banyan network is a variation of the classical banyan network in two ways: (1) each node is a processor with a switch, and (2) every pair of nodes at the two ends is merged. We present a routing algorithm for the cylindrical banyan network, and show it is optimal in terms of the path length. We also show that for the cylindrical banyan network containing L levels with 2L processors at each level (i.e., containing L2L processors in total), the worst case path length between any two nodes is 1.5L. We discuss a generalization of the cylindrical banyan network and an optimal routing algorithm for it. Our routing algorithms are distributed, and so can be executed locally at each processor.
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