This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Fault-Tolerant Embedding of Complete Binary Trees in Hypercubes
March 1993 (vol. 4 no. 3)
pp. 277-288

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.

[1] S. Bhatt, F. Chung, T. Leighton, and A. Rosenberg, "Optimal simulations of tree machines," inProc. 27th Annu. Symp. Foundations Comput. Sci., 1986, pp. 274-282.
[2] S. N. Bhatt and I. C. F. Ipsen, "How to embed trees in hypercubes," Tech. Rep. YALEU/DCS/RR-443, Yale Univ., Dec. 1985.
[3] M. Y. Chan, F. Y. L. Chin, and C. K. Poon, "Optimal simulation of full binary trees on faulty hypercubes," inProc. 2nd Annu. Int. Symp. Algorithms, 1991.
[4] M. Y. Chan and S-J. Lee, "Distributed fault-tolerant embeddings of rings in hypercubes,"J. Parallel Distributed Comput., vol. 11, pp. 63-71 1991.
[5] J. Hastad, T. Leighton, and M. Newman, "Reconfiguring a hypercube in the presence of faults," inProc. 19th Annu. ACM Symp. Theory of Computing, May 1987, pp. 274-284.
[6] J. Hastad, T. Leighton, and M. Newman, "Fast computation using faulty hypercubes," inProc. 21st Annu. ACM Symp. Theory Comput., May 1989, pp. 251-263.
[7] F. J. Provost and R. Melhem, "Distributed fault tolerant embedding of binary trees and rings in hypercubes, " inProc. Int. Workshop Defect and Fault Tolerance in VLSI Syst., 1988, pp. 8.3.1-8.3.8.
[8] A. Wang, R. Cypher, and E. Mayr, "Embedding complete binary trees in faulty hypercubes," IBM Tech. Rep. RJ 7821(72203), Nov. 1990.
[9] A. Wu, "Embedding of tree networks into hypercubes,"J. Parallel Distributed Comput., vol. 2, pp. 238-249 1985.

Index Terms:
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)
Citation:
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, doi:10.1109/71.210811
Usage of this product signifies your acceptance of the Terms of Use.