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Processor Allocation in Hypercube Multicomputers: Fast and Efficient Strategies for Cubic and Noncubic Allocation
October 1995 (vol. 6 no. 10)
pp. 1108-1122

Abstract—A new approach for dynamic processor allocation in hypercube multicomputers which supports a multi-user environment is proposed. A dynamic binary tree is used for processor allocation along with an array of free lists. Two algorithms are proposed based on this approach, capable of efficiently handling cubic as well as noncubic allocation. Time complexities for both allocation and deallocation are shown to be polynomial, a significant improvement over the existing exponential and even super-exponential algorithms. Unlike existing schemes, the proposed strategies are best-fit strategies within their search space. Simulation results indicate that the proposed strategies outperform the existing ones in terms of parameters such as average delay in honoring a request, average allocation time, average deallocation time, and memory overhead.

[1] A. Al-Dhelaan and B. Bose,“A new strategy for processor allocation in an n-cube multiprocessor,” Proc. Int’l Phoenix Conf. Computers and Comm., pp. 114-118, Mar. 1989.
[2] S. Baase, Computer Algorithms: Introduction to Design and Analysis, second ed. Addison-Wesley, 1991.
[3] M. S. Chen and K. G. Shin,“Processor allocation in an$N$-cube multiprocessor using gray codes,”IEEE Trans. Comput., vol. C-37, pp. 1396–1407, Dec. 1987.
[4] M.S. Chen and K.G. Shin, "Task Migration in Hypercube Multiprocessors," Proc. 16th Int'l Symp. Computer Architecture, pp. 105-111, May 1989.
[5] M.S. Chen and K.G. Shin, "Subcube Allocation and Task Migration in Hypercube Multiprocessors," IEEE Trans. Computers, vol. 39, no. 9, pp. 1,146-1,155, Sept. 1990.
[6] P.J. Chuang and N.F. Tzeng, "Dynamic Processor Allocation in Hypercube Computers," Proc. 17th Ann. Int'l Symp. Computer Architecture, May 1990.
[7] D. Das Sharma and D.K. Pradhan,“A novel approach for subcube allocation inhypercube multiprocessors,” Proc. Fourth IEEE Symp. Parallel andDistributed Systems, pp. 336-345, Dec. 1992.
[8] D. Das Sharma and D.K. Pradhan,“Fast and efficient strategies for cubicand noncubic allocation in hypercube multiprocessors,” Int’l Conf. Parallel Processing, vol. I, pp. 118-127, Aug. 1993.
[9] D. Das Sharma and D.K. Pradhan, “A Fast and Efficient Strategy for Submesh Allocation in Mesh-Connected Parallel Computers,” Proc. Fifth IEEE Symp. Parallel and Distributed Processing, pp. 682-689, Dec. 1993.
[10] D. Das Sharma and D.K. Pradhan,“Job scheduling in mesh multicomputers,” 1994 Int’l Conf. Parallel Processing.
[11] D. Das Sharma,G.D. Holland,, and D.K. Pradhan,“Subcube level time-sharingin hypercube multicomputers,” 1994 Int’l Conf. Parallel Processing.
[12] D. Das Sharma and D.K. Pradhan,“Novel strategies for cubic and noncubicallocation in hypercube multiprocessors,” Technical Report TR-93-023, Dept. of Computer Science, Texas A&M Univ.
[13] S. Dutt and J.P. Hayes,“On allocating subcubes in a Hhpercubemultiprocessor,” Proc. Third Conf. Hypercube Computers and Applications, pp. 801-810, Jan. 1988.
[14] C. Hu,M. Bayoumi,B. Kearfott,, and Q. Yng,“A parallelized algorithm forthe the preconditioned interval newton method,” Proc. Fifth SIAM Conf. Parallel Processing for Scientific Computing, Mar. 1991.
[15] J. Kim, C.R. Das, and W. Lin, “A Top-Down Processor Allocation Scheme for Hypercube Computers,” IEEE Trans. Parallel and Distributed Systems, vol. 2, no. 1, pp. 20-30, Jan. 1991.
[16] J. Kim,C.R. Das,, and W. Lin,“A processor allocation scheme for hypercube computers,” Proc. 1989 Int’l Conf. Parallel Processing, vol. II, pp. 231-238, Aug. 1989.
[17] E. Horowitz and S. Sahni, Fundamentals of Data Structures in Pascal. Rockville, Md.: Computer Science Press, 1989.
[18] K.C. Knowlton, “A Fast Storage Allocator,” Comm. ACM, vol. 8, pp. 623-625, Oct. 1965.
[19] D. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching. Addison-Wesley, 1973.
[20] P. Krueger,T.-H. Lai,, and V.A. Radiya,“Processor allocation vs. job scheduling on hypercube computers,” Proc. 11th Int’l Conf. Distributed Computing Systems,Arlington, Tex., pp. 394-401, 1991.
[21] nCUBE 2 Systems: Technical Overview, nCUBE Corp., Foster City, Calif., 1992.
[22] K.S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications. Prentice Hall, 1982.
[23] N.-F. Tzeng,H.L. Chen,, and P.J. Chuang,“Embeddings in incompletehypercube,” Proc. 1990 Int’l Conf. Parallel Processing, Aug. 1990.
[24] H. Wang and Q. Yang,“Prime cube graph approach for processor allocation inhypercube multiprocessors,” Proc. 1991 Int’l Conf. Parallel Processing, vol. I, pp. 25-32.

Index Terms:
Cubic allocation, deallocation, dynamic binary tree, fragmentation, hypercube, noncubic allocation.
Debendra Das Sharma, Dhiraj K. Pradhan, "Processor Allocation in Hypercube Multicomputers: Fast and Efficient Strategies for Cubic and Noncubic Allocation," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 10, pp. 1108-1122, Oct. 1995, doi:10.1109/71.473519
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