This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
The Extended Cube Connected Cycles: An Efficient Interconnection for Massively Parallel Systems
May 1996 (vol. 45 no. 5)
pp. 609-614

Abstract—The hypercube structure is a very widely used interconnection topology because of its appealing topological properties. For massively parallel systems with thousands of processors, the hypercube suffers from a high node fanout which makes such systems impractical and infeasible. In this paper, we introduce an interconnection network called The Extended Cube Connected Cycles (ECCC) which is suitable for massively parallel systems. In this topology the processor fanout is fixed to four. Other attractive properties of the ECCC include a diameter of logarithmic order and a small average interprocessor communication distance which imply fast data transfer. The paper presents two algorithms for data communication in the ECCC. The first algorithm is for node-to-node communication and the second is for node-to-all broadcasting. Both algorithms take O(log N) time units, where N is the total number of processors in the system. In addition, the paper shows that a wide class of problems, the divide and conquer class, is easily and efficiently solvable on the ECCC topology. The solution of a divide and conquer problem of size N requires O(log N) time units.

[1] V. Benes,Mathematical Theory of Connecting Networks and Telephone Traffic.New York: Academic Press, 1965.
[2] K.V. Bhat,"On Properties of Arbitrary Hypercubes," Comp,&Maths with Appls., vol. 8, no. 1, pp. 31-42, 1982.
[3] S.P. Dandamudi and D.L. Eager, "Hierarchical Interconnection Networks for Multicomputer Systems," IEEE Trans. Computers, pp. 786-797, 1990.
[4] A. El-Amawy and S. Latifi, "Properties and Performance of Folded Hypercubes," IEEE Trans. Parallel and Distributed Systems, vol. 2, no. 1, pp. 31-42, 1991.
[5] C.M. Fiduccia,“Bused hypercubes and other pin-optimal networks,” IEEE Trans. Parallel and Distributed Systems, vol. 3, pp. 14-24, 1992.
[6] K. Hwang and J. Ghosh, "Hypernet: A Communication Efficient Architecture for Constructing Massively Parallel Computers," IEEE Trans. Computers, pp. 1,450-1,466, 1987.
[7] O.H. Ibarra and S.M. Sohn, "On Mapping Systolic Algorithms onto the Hypercube," IEEE Trans. Parallel and Distributed Systems, vol. 1, no. 1, pp. 48-63, Jan. 1990.
[8] S.L. Johnsson and C.T. Ho,“Spanning graphs for optimum broadcasting and personalizedcommunication in hypercubes,” IEEE Trans. Computers, vol. 38, no. 9, pp. 1,249-1,268, Sept. 1989.
[9] H.P. Katseff, "Incomplete Hypercubes," IEEE Trans. Computers, vol. 37, no. 5, pp. 604-608, May 1988.
[10] J.M. Kumar and L.M. Patnaik, "Extended Hypercube: A Hierarchical Interconnection Network of Hypercubes," IEEE Trans. Parallel and Distributed Systems, pp. 45-57, 1992.
[11] F.P. Preparata and J. Vuillemin, “The Cube-Connected Cycles: A Versatile Network for Parallel Computation,” Comm ACM, vol. 24, no. 5, pp. 300-309, 1981.
[12] Q.M. Malluhi and M.A. Bayoumi, "The Hierarchical Hypercube: A New Interconnection Topology for Massively Parallel Systems," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 1, pp. 17-30, Jan. 1994.
[13] Y. Saad and M.H. Schultz, "Data Communication in Hypercubes," J. Parallel and Distributed Computing, vol. 6, pp. 115-135, 1989.
[14] Y. Saad and M. Schultz, "Topological Properties of Hypercubes," IEEE Trans. Computers, vol. 37, no. 7, pp. 867-872, July 1988.
[15] H.S. Stone,"Parallel Processing with Perfect Shuffle," IEEE Trans. Computers, vol. 20, no. 2, Feb. 1971.
[16] A. Youssef and B. Narahari, "Banyan-Hypercube Networks," IEEE Trans. Parallel and Distributed Systems, vol. 1, no. 2, pp. 160-169, Apr. 1990.

Index Terms:
Hypercube, cube connected cycles, routing, broadcasting, interconnection network, divide and conquer.
Citation:
R.a. Ayoubi, Q.m. Malluhi, M.a. Bayoumi, "The Extended Cube Connected Cycles: An Efficient Interconnection for Massively Parallel Systems," IEEE Transactions on Computers, vol. 45, no. 5, pp. 609-614, May 1996, doi:10.1109/12.509913
Usage of this product signifies your acceptance of the Terms of Use.