This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Subcube Allocation and Task Migration in Hypercube Multiprocessors
September 1990 (vol. 39 no. 9)
pp. 1146-1155

Two important issues in managing processors in a hypercube are addressed: subcube allocation and task migration to eliminate the system fragmentation caused by allocation and deallocation of subcubes. It is proven that the subcube allocation strategy using a binary reflected Gray code (BRGC), called the GC strategy, possesses the best subcube recognition ability among all strategies using sequential searches. A binary code (BC) is defined as the binary representation of a nonnegative integer, and an extended binary code (EBC) is obtained by permutating the bits of a BC. Similarly, an extended Gray code (EGC) is obtained from a BRGC. The subcube recognition ability of an allocation strategy using multiple EBCs is analyzed and compared to that using multiple EGCs.

[1] T. F. Chan and Y. Saad, "Multigrid algorithms on the hypercube multiprocessor,"IEEE Trans. Comput., vol. C-35, no. 11, pp. 969-977, Nov. 1986.
[2] Y. Saad and M. H. Schultz, "Topological properties of hypercubes,"IEEE Trans. Comput., vol. C-37, no. 7, pp. 867-872, July 1988.
[3] M.-S. Chen and K. G. Shin, "Processor allocation in anN-cube multiprocessorusing Gray codes,"IEEE Trans. Comput., vol. C-36, no. 12, pp. 1396-1407, Dec. 1987.
[4] M.-S. Chen and K. G. Shin, "On relaxed squashed embedding of graphs a into hypercube,"SIAM J. Comput., vol. 18, no. 6, pp. 1226-1244, Dec. 1989.
[5] C. L. Seitz, "The Cosmic Cube,"Commun. ACM, pp. 22-33, Jan. 1985.
[6] N. Corp.,NCUBE/ten: An Overview, Nov. 1985.
[7] S. L. Johnsson, "Communication efficient basic linear algebra computations on hypercube architectures,"J. Parallel Distributed Comput., pp. 133-172, 1987.
[8] K. C. Knowlton, "A fast storage allocator,"Commun. ACM, vol. 8, no. 10, pp. 623-625, Oct. 1965.
[9] F. Harary,Graph Theory. Reading, MA: Addison-Wesley, 1969.
[10] C. L. Liu,Introduction to Combinatorial Mathematics. New York: McGraw-Hill, 1968.
[11] D. E. Knuth,The Art of Computer Programming, Vol. 1. Reading, MA: Addison-Wesley, 1973.
[12] E. M. Reingold, J. Nievergelt, and N. Deo,Combinatorial Algorithm. Englewood Cliffs, NJ: Prentice-Hall, 1977.

Index Terms:
task migration; hypercube multiprocessors; subcubes; binary reflected Gray code; BRGC; GC strategy; subcube recognition; binary code; extended binary code; EBC; extended Gray code; EGC; multiprocessing systems.
Citation:
M.-S. Chen, K.G. Shin, "Subcube Allocation and Task Migration in Hypercube Multiprocessors," IEEE Transactions on Computers, vol. 39, no. 9, pp. 1146-1155, Sept. 1990, doi:10.1109/12.57056
Usage of this product signifies your acceptance of the Terms of Use.