121 research outputs found
Wildcard dimensions, coding theory and fault-tolerant meshes and hypercubes
Hypercubes, meshes and tori are well known interconnection networks for parallel computers. The sets of edges in those graphs can be partitioned to dimensions. It is well known that the hypercube can be extended by adding a wildcard dimension resulting in a folded hypercube that has better fault-tolerant and communication capabilities. First we prove that the folded hypercube is optimal in the sense that only a single wildcard dimension can be added to the hypercube. We then investigate the idea of adding wildcard dimensions to d-dimensional meshes and tori. Using techniques from error correcting codes we construct d-dimensional meshes and tori with wildcard dimensions. Finally, we show how these constructions can be used to tolerate edge and node faults in mesh and torus networks
Star Structure Connectivity of Folded hypercubes and Augmented cubes
The connectivity is an important parameter to evaluate the robustness of a
network. As a generalization, structure connectivity and substructure
connectivity of graphs were proposed. For connected graphs and , the
-structure connectivity (resp. -substructure connectivity
) of is the minimum cardinality of a set of subgraphs
of that each is isomorphic to (resp. to a connected subgraph of ) so
that is disconnected or the singleton. As popular variants of hypercubes,
the -dimensional folded hypercubes and augmented cubes are
attractive interconnected network prototypes for multiple processor systems. In
this paper, we obtain that
for , , and
for
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