Embedding n-Dimensional Crossed Hypercube into Pancake Graphs
M. F. Zerarka
Polytechnic Engineers School Labs E.P.F. 3 bis street Lakanal, 92330 Sceaux, France.
S. Femmam *
Polytechnic Engineers School Labs E.P.F. 3 bis street Lakanal, 92330 Sceaux, France & University of UHA France.
R. Aschheim
Polytopics Research Institute, 8 villa Haussmann, 92130 Issy, France.
*Author to whom correspondence should be addressed.
Abstract
Among Cayley graphs on the symmetric group, the pancake graph is one as a viable interconnection scheme for parallel computers, which has been examined by a number of researchers. The pancake was proposed as alternatives to the hypercube for interconnecting processors in parallel computers. Some good and attractive properties of this interconnection network include: vertex symmetry, small degree, a sub-logarithmic diameter, extendability, and high connectivity (robustness), easy routing, and regularity of topology, fault tolerance, extensibility and embeddability of other topologies. In this paper, we present the many-to-one dilation 5 embedding of n-dimensional crossed hypercube into n-dimensional pancake patients. These predictors, however, need further work to validate reliability.
Keywords: Cayley graph, embedding, crossed hypercube networks, pancake networks, dilation.