Title :
Isomorphism of degree four Cayley graph and wrapped butterfly and their optimal permutation routing algorithm
Author :
Wei, David S L ; Muga, Felix P., II ; Naik, Kshirasagar
Author_Institution :
Dept. of Comput. & Inf. Sci., Fordham Univ., New York, NY, USA
fDate :
12/1/1999 12:00:00 AM
Abstract :
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(√N), where N is the network size
Keywords :
computational complexity; graph theory; multiprocessor interconnection networks; parallel algorithms; degree four Cayley graph; edge-preserving bijective mapping; optimal permutation routing algorithm; topological properties; wrapped butterfly; Algorithm design and analysis; Availability; Hypercubes; Multiprocessor interconnection networks; Routing;
Journal_Title :
Parallel and Distributed Systems, IEEE Transactions on
