A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
On the problem of sorting burnt pancakes
Discrete Applied Mathematics
Shortest routing in trivalent Cayley graph network
Information Processing Letters
On the diameter of the pancake network
Journal of Algorithms
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
A Class of Fixed-Degree Cayley-Graph Interconnection Networks Derived by Pruning k-ary n-cubes
ICPP '97 Proceedings of the international Conference on Parallel Processing
Embedding hypercubes into pancake, cycle prefix and substring reversal networks
HICSS '95 Proceedings of the 28th Hawaii International Conference on System Sciences
A New Fixed Degree Regular Network for Parallel Processing
SPDP '96 Proceedings of the 8th IEEE Symposium on Parallel and Distributed Processing (SPDP '96)
On The Shuffle-Exchange Permutation Network
ISPAN '97 Proceedings of the 1997 International Symposium on Parallel Architectures, Algorithms and Networks
Graph Theory With Applications
Graph Theory With Applications
Computing the diameter of 17-pancake graph using a PC cluster
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
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Cayley networks have desirable properties for interconnection networks, but the degree of many well-known Cayley networks grows with the number of nodes. Therefore, fixed-degree Cayley networks have also been introduced. We consider fixed-degree Cayley networks which are also subnetworks of the pancake network Pn. The pancake problem concerns the number of prefix reversals or "flips," required to sort a permutation of length n. This is also the diameter of Pn. Restricting the problem to three of the n - 1 possible flips, generates a subnetwork of Pn. We identify proper subnetworks and spanning subnetworks of Pn generated by three flips. We introduce a degree 3 spanning subnetwork of Pn, the Triad network, or Triadn. When n is odd and n mod 8 ≠ 1, Triadn has n! nodes and diameter Θ(n log n). Triadn emulates the shuffle-exchange and shuffle-exchange permutation networks with constant slowdown.