Publication 1995 Issue No. 1 - January Abstract - Wildcard Dimensions, Coding Theory and Fault-Tolerant Meshes and Hypercubes
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Wildcard Dimensions, Coding Theory and Fault-Tolerant Meshes and Hypercubes
January 1995 (vol. 44 no. 1)
pp. 150-155
 ASCII Text x Jehoshua Bruck, Robert Cypher, Ching-Tien Ho, "Wildcard Dimensions, Coding Theory and Fault-Tolerant Meshes and Hypercubes," IEEE Transactions on Computers, vol. 44, no. 1, pp. 150-155, January, 1995.
 BibTex x @article{ 10.1109/12.367998,author = {Jehoshua Bruck and Robert Cypher and Ching-Tien Ho},title = {Wildcard Dimensions, Coding Theory and Fault-Tolerant Meshes and Hypercubes},journal ={IEEE Transactions on Computers},volume = {44},number = {1},issn = {0018-9340},year = {1995},pages = {150-155},doi = {http://doi.ieeecomputersociety.org/10.1109/12.367998},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Wildcard Dimensions, Coding Theory and Fault-Tolerant Meshes and HypercubesIS - 1SN - 0018-9340SP150EP155EPD - 150-155A1 - Jehoshua Bruck, A1 - Robert Cypher, A1 - Ching-Tien Ho, PY - 1995VL - 44JA - IEEE Transactions on ComputersER -

Abstract—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.

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Citation:
Jehoshua Bruck, Robert Cypher, Ching-Tien Ho, "Wildcard Dimensions, Coding Theory and Fault-Tolerant Meshes and Hypercubes," IEEE Transactions on Computers, vol. 44, no. 1, pp. 150-155, Jan. 1995, doi:10.1109/12.367998