A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Hamiltonian decomposition of Cayley graphs of degree 4
Journal of Combinatorial Theory Series B
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Packet routing and PRAM emulation on star graphs and leveled networks
Journal of Parallel and Distributed Computing
A New Family of Cayley Graph Interconnection Networks of Constant Degree Four
IEEE Transactions on Parallel and Distributed Systems
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
Comments on "A New Family of Cayley Graph Interconnection Networks of Constant Degree Four"
IEEE Transactions on Parallel and Distributed Systems
Routing, merging and sorting on parallel models of computation
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Some characterizations for the wrapped butterfly
Analysis, combinatorics and computing
A new family of interconnection networks of odd fixed degrees
Journal of Parallel and Distributed Computing - Special issue: 18th International parallel and distributed processing symposium
A practical peer-performance-aware DHT
AP2PC'04 Proceedings of the Third international conference on Agents and Peer-to-Peer Computing
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In this paper, we first show that the degree four Cayley graph proposed in a paper appearing in the January 1996 issue of IEEE Transactions on Parallel and Distributed Systems is indeed isomorphic to the wrapped butterfly. The isomorphism was first reported by Muga and Wei in the proceedings of PDPTA "96.The isomorphism is shown by using an edge-preserving bijective mapping. Due to the isomorphism, algorithms for the degree four Cayley graph can be easily developed in terms of wrapped butterfly and topological properties of one network can be easily derived in terms of the other. Next, we present the first optimal oblivious one-to-one permutation routing scheme for these networks in terms of the wrapped butterfly. Our algorithm runs in time $O(\sqrt{N})$, where $N$ is the network size.