This Article 
 Bibliographic References 
 Add to: 
Operationally Enhanced Folded Hypercubes
December 1994 (vol. 5 no. 12)
pp. 1310-1316

Recently, several variations of the hypercube have been proposed to enhance itsperformance and reliability. The folded hypercube is one of these variations, in which anextra link is added to each node providing a direct connection to the node locatedfarthest from it. In this paper, we propose a new operation mode of the folded hypercubeto enhance its performance and fault-tolerance. There are (/sub ksup n+1/) regulark-cubes within a folded hypercube of dimension n, denoted by FQ/sub n/. We introduceanother type of hypercube, called the twisted hypercube, to improve the performanceand fault tolerance of the folded hypercube. The problems of finding a subcube of givensize in an FQ/sub n/ and routing messages within the subcube are addressed for theproposed operation mode. The advantages of the proposed operation mode over theregular-hypercube operation mode are analyzed in terms of dependability and robustness.The proposed operation mode is shown to make significant improvements over theregular-hypercube operation mode in both dependability and robustness. Because thenew operation mode can be applied to only an (n-1)-subcube level for a given FQ/sub n/,we present general form of folded hypercube, thus enhancing the availability of subcubesof any dimension m>n.

[1] Y. Saad and M. H. Schultz, "Topological properties of hypercube,"IEEE Trans. Comput., vol. C-37, pp. 867-872, July 1988.
[2] F. P. Preparata and J. Vuillemin, "The cube-connected cycle: A versatile network for parallel computation,"Commun. ACM, vol. 24, pp. 300-309, May 1981.
[3] A. Esfahanian, L. M. Ni, and B. E. Sagan, "On enhancing hypercube multiprocessors," inProc. 1988 ICPP, 1988, pp. 86-89.
[4] F. J. Meyer and D. K. Pradhan, "Flip-trees: Fault tolerant graphs with wide containers,"IEEE Trans. Comput., vol. C-37, pp. 472-478, Apr. 1988.
[5] S. Latifi and A. El-Amawy, "On folded hypercubes," inProc. 1989 ICPP, 1989, pp. 180-187.
[6] S. Latifi, "The efficiency of the folded hypercube in subcube allocation," inProc. 1990 ICPP, vol. I, pp. 218-225, Aug. 1990.
[7] S. Latifi, "Fault-tolerant hypercube multiprocessors,"IEEE Trans. Reliability, vol. 39, pp. 361-367, Aug. 1990.
[8] C. T. Ho, "Full bandwidth communications on folded hypercubes," inProc. 1990 ICPP, vol. I, pp. 276-280, Aug. 1990.
[9] L. N. Bhuyan and D. P. Agrawal, "Generalized hypercube and hyperbus structures for a computer network,"IEEE Trans. Comput., 1984, pp. 323-333.
[10] W.J. Dally and C.L. Seitz, "Deadlock-Free Message Routing in Multiprocessor Interconnection Networks,"IEEE Trans. Computers, Vol. C-36, No. 5, May 1987, pp. 547-553.
[11] K. Jim and C. R. Das, "On subcube dependability in a hypercube," inProc. ACM SIGMETRICS'91, 1991, pp. 111-119.
[12] S. Abraham and K. Padmanabhan, "Reliability of the hypercube," inProc. 1988 ICPP, vol. I, pp. 90-94, Aug. 1988.
[13] N. F. Tzeng and S. Wei, "Enhanced hypercubes,"IEEE Trans. Comput., vol. 40, pp. 284-294, Mar. 1991.

Index Terms:
Index Termshypercube networks; performance evaluation; fault tolerant computing; reliability;operationally enhanced folded hypercubes; performance; reliability; operation mode;fault-tolerance; twisted hypercube
J. Kim, K.G. Shin, "Operationally Enhanced Folded Hypercubes," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 12, pp. 1310-1316, Dec. 1994, doi:10.1109/71.334904
Usage of this product signifies your acceptance of the Terms of Use.