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Proceedings., 33rd Annual Symposium on Foundations of Computer Science (1992)
Pittsburgh, PA, USA
Oct. 24, 1992 to Oct. 27, 1992
ISBN: 0-8186-2900-2
pp: 533-541
H. Tamaki , Dept. of Comput. Sci., Toronto Univ., Ont., Canada
The author studies the embedding of the butterfly network in a faulty version of itself where each node is independently faulty with some constant probability. He shows that such a self-embedding of the N-node butterfly with O(1) load, O((log logN)/sup 2.6/) dilation, and 0((log log N)/sup 8.2/) congestion is possible with high probability, assuming sufficiently small node-failure probability. This embedding is level-preserving in the sense that each node is mapped to a node in the same level of the butterfly. He also derives a lower bound of log log log N-c on the dilation of a level-preserving embedding with O(log/sup alpha / N) load, for any alpha , 0< alpha <1, any node-failure probability p>0, and some constant c depending on alpha and p.
level-preserving embedding, self-embedding, butterfly networks, random faults, dilation, congestion, node-failure probability

H. Tamaki, "Efficient self-embedding of butterfly networks with random faults," Proceedings., 33rd Annual Symposium on Foundations of Computer Science(FOCS), Pittsburgh, PA, USA, 1992, pp. 533-541.
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