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Expected Capacity of (m2)-Networks
July 1983 (vol. 32 no. 7)
pp. 649-657
G.M. Masson, Department of Electrical Engineering and Computer Science, Johns Hopkins University
A concentrator is an interconnection network with n inputs and m outputs, n > m, wherein any specified subset of inputs of size less than or equal to some number, called the network's actual capacity, can always be simultaneously connected to some equal-sized but unspecifiable subset of outputs. Guaranteed throughput as described by actual capacity has heretofore been the principle measure for evaluating concentrator performance. In many applications, however, a more practical measure of a concentrator's capability is a probabilistic measure of its throughput in the following sense: given an input subset of size k, k = m, what is the average number of inputs that can be connected to outputs? This measure will be called expected capacity. This paper considers the expected capacity of a special class of sparse crossbar concentrators called ( m 2 ) networks. It is seen that the expected capacity values for ( m 2 ) networks are usually quite close to k.
Index Terms:
prime decomposition, Actual capacity, binomial networks, concentrator, expected capacity, ( m 2 ) networks, prime component counts
G.M. Masson, S.B. Morris, "Expected Capacity of (m2)-Networks," IEEE Transactions on Computers, vol. 32, no. 7, pp. 649-657, July 1983, doi:10.1109/TC.1983.1676296
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