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Extra info for Advanced Computer Architecture and Parallel Processing
The radix implies that there are k nodes in each dimension. An 8-ary 1-cube is simply an eight node ring, while an 8-ary 2-cube is eight 8-node rings connected such that nodes are connected to all nodes with an address that differs in only one digit (see TEAM LinG - Live, Informative, Non-cost and Genuine ! 19 Examples of k-ary n-cube networks (a) 8-ary 1-cube (8 nodes ring) network; and (b) 8-ary 2-cube (eight 8-node rings) network. Fig. 19). It should be noted that the number of nodes in a k-ary n-cube is N ¼ kn nodes and that when k ¼ 2, the architecture becomes a binary n-cube.
The degree of a node in a binary tree is 3, that is, O(1), while the diameter is O( log2 N). Cube-Connected Networks An n-cube network has 2n nodes where two nodes are connected if the binary representation of their addresses differs by one and only one bit. The cost (complexity) of an n-cube measured in terms of the number of nodes in the cube is O(2n ) while the delay (latency) measured in terms of the number of nodes traversed while going from a source node to a destination node is O( log2 N).
REFERENCES Abraham, S. and Padmanabhan, K. Performance of the direct binary n-cube network for multiprocessors. IEEE Transactions on Computers, 38 (7), 1000– 1011 (1989). , Janakiram, V. and Pathak, G. Evaluating the performance of multicomputer conﬁgurations. IEEE Transaction on Computers, 19 (5), 23 – 27 (1986). Almasi, G. and Gottlieb, A. Highly Parallel Computing, Benjamin Cummings, 1989. , Abd-El-Barr, M. and Ashraf, F. A survey and comparison of wormhole routing techniques in mesh networks.