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Highly reliable symmetric networks

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2 Author(s)
Huisman, L.M. ; IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA ; Kundu, S.

We generalize directed loop networks to loop-symmetric networks in which there are N nodes and in which each node has in-degree and out-degree k, subject to the condition that 2k does not exceed N. We show that by proper selection of links one can obtain generalized loop networks with optimal or close to optimal diameter and connectivity. The optimized diameter is less than k[N1k/], where [x] indicates the ceiling of x. We also show that these networks are rather compact in that the diameter is not more than twice the average distance. Roughly 1/2(k-1)N1k/ nodes can be removed such that the network of remaining nodes is still strongly connected, if all remaining nodes have at least one incoming and one outgoing link left

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Parallel and Distributed Systems, IEEE Transactions on  (Volume:5 ,  Issue: 1 )