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| M.Y. Chan, S.J. Lee, "Fault-Tolerant Embedding of Complete Binary Trees in Hypercubes," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 3, pp. 277-288, March, 1993. | |||
| BibTex | x | ||
| @article{ 10.1109/71.210811, author = {M.Y. Chan and S.J. Lee}, title = {Fault-Tolerant Embedding of Complete Binary Trees in Hypercubes}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {4}, number = {3}, issn = {1045-9219}, year = {1993}, pages = {277-288}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.210811}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Parallel and Distributed Systems TI - Fault-Tolerant Embedding of Complete Binary Trees in Hypercubes IS - 3 SN - 1045-9219 SP277 EP288 EPD - 277-288 A1 - M.Y. Chan, A1 - S.J. Lee, PY - 1993 KW - Index Termsfault tolerant embedding; complete binary trees; hypercubes; graph-theoretic question;simulation; k-tree; NP-complete; upper bound; computational complexity; fault tolerantcomputing; hypercube networks; trees (mathematics) VL - 4 JA - IEEE Transactions on Parallel and Distributed Systems ER - | |||
The focus is on the following graph-theoretic question associated with the simulation ofcomplete binary trees by faulty hypercubes: if a certain number of nodes or links areremoved from an n-cube, will an (n-1)-tree still exists as a subgraph? While the generalproblem of determining whether a k-tree, k>n, still exists when an arbitrary number ofnodes/links are removed from the n-cube is found to be NP-complete, an upper bound isfound on how many nodes/links can be removed and an (n-1)-tree still be guaranteed toexist. In fact, as a corollary of this, it is found that if no more than n-3 nodes/links areremoved from an (n-1)-subcube of the n-cube, an (n-1)-tree is also guaranteed to exist.
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