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Highly Reliable Symmetric Networks
January 1994 (vol. 5 no. 1)
pp. 94-97

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

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Index Terms:
Index Termslocal area networks; reliability; highly reliable symmetric networks; directed loopnetworks; loop-symmetric networks; generalized loop networks; connectivity; local areanetworks
L.M. Huisman, S. Kundu, "Highly Reliable Symmetric Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 1, pp. 94-97, Jan. 1994, doi:10.1109/71.262592
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