Complexity issues in VLSI: optimal layouts for the shuffle-exchange graph and other networks
Complexity issues in VLSI: optimal layouts for the shuffle-exchange graph and other networks
Work-preserving emulations of fixed-connection networks
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Group action graphs and parallel architectures
SIAM Journal on Computing
On the computational equivalence of hypercube-derived networks
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Journal of the ACM (JACM)
Is the Shuffle-Exchange Better Than the Butterfly?
ISA '91 Proceedings of the 2nd International Symposium on Algorithms
| Hi-index | 14.98 |
One of the first theorems on permutation routing, proved by V.E. Benes (1965), shows that give a set of source-destination pairs in an N-node butterfly network with at most a constant number of sources or destinations in each column of the butterfly, there exists a set of paths of lengths O(log N) connecting each pair such that the total congestion is constant. An analogous theorem yielding constant-congestion paths for off-line routing in the shuffle-exchange graph is proved here. The necklaces of the shuffle-exchange graph play the same structural role as the columns of the butterfly in the Benes theorem.