Processor allocation and task scheduling of matrix chain products on parallel systems

IEEE Transactions on Parallel and Distributed Systems

Volumn 14, Issue 4, 2003, Pages 394-407

  Lee, Heejo ^a   Kim, Jong ^b   Hong, Sung Je ^b   Lee, Sunggu ^b  

^a Ahnlab Inc   (South Korea)

^b Pohang University of Science and Technology (POSTECH)   (South Korea)

Author keywords

Matrix chain product; Matrix chain scheduling problem; Parallel matrix multiplication; Processor allocation; Task scheduling

Indexed keywords

ALGORITHMS; MATRIX ALGEBRA; PROGRAM PROCESSORS; SCHEDULING;

MATRIX CHAIN PRODUCTS;

PARALLEL PROCESSING SYSTEMS;

EID: 0037619247     PISSN: 10459219     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPDS.2003.1195411     Document Type: Article

References (33)

1. E. Horowitz and S. Sahni, Fundamentals of Data Structures, Potomac, Md.: Computer Science Press, 1976.
2. E. Dekel, D. Nassimi, and S. Sahni, "Parallel Matrix and Graph Algorithms," SIAM J. Computing, vol. 10, pp. 657-675, Nov. 1981.
3. S.-T. Yau and Y.Y. Lu, "Reducing the Symmetric Matrix Eigenvalue Problem to Matrix Multiplications," SIAM J. Scientific Computing, vol. 14, no. 1, pp. 121-136, 1993.
4. S.-S. Lin, "A Chained-Matrices Approach for Parallel Computation of Continued Fractions and Its Applications," J. Scientific Computing, vol. 9, no. 1, pp. 65-80, 1994.
5. V. Kumar, A. Grama, A. Gupta, and G. Karypis, Introduction to Parallel Computing: Design and Analysis of Parallel Algorithms. Benjamin/Cummings, 1994.
6. A. Chandra, "Computing Matrix Chain Products in Near-Optimal Time," technical report, IBM T.J. Watson Research Center, Yorktown Heights, N.Y., IBM Research Report RC 5625(#24393), 1975.
7. H. Gould, Bell and Catalan Numbers, Research Inst., Morgantown, W.Va., June 1977.
8. S. Godbole, "An Efficient Computation of Matrix Chain Products," 'IEEE Trans. Computers, pp. 864-866, vol. 22, no. 9, Sept. 1973.
9. F. Chin, "An O(n) Algorithm for Determining a Near-Optimal Computation Order of Matrix Chain Product," Comm. ACM, pp. 544-549, 1978.
10. T. Hu and M. Shing, "Computation of Matrix Chain Products. Part I," SIAM J. Computing, vol, 11, pp. 362-373, May 1982.
11. T. Hu and M. Shing, "Computation of Matrix Chain Products. Part II," SIAM J. Computing, vol. 13, pp. 228-251, May 1984.
12. P. Ramanan, "A New Lower Bound Technique and Its Application: Tight Lower Bound for a Polygon Triangulation Problem," SIAM J. Computing, vol. 23, pp. 834-851, Aug. 1994.
13. L. Valiant, S. Skyum, S. Berkowitz, and C. Rackoff, "Fast Parallel Computation of Polynomials Using Few Processors," SIAM J. Computing, vol. 12, pp. 641-644, 1983.
14. W. Rytter, "Note on Efficient Parallel Computations for Some Dynamic Programming Problems," Theoretical Computer Science, vol. 59, pp. 297-307, 1988.
15. S.-H.S. Huang, H. Liu, and V. Viswanathan, "Parallel Dynamic Programming," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 3, pp. 326-328, Mar. 1994.
16. P.G. Bradford, G.J. Rawlins, and G.E. Shannon, "Efficient Matrix Chain Ordering in Polylog Time," SIAM J. Computing, vol. 27, no. 2, pp. 466-490, 1998.
17. A. Czumaj, "Parallel Algorithm for the Matrix Chain Product and the Optimal Triangulation Problems," Proc. Symp. Theoretical Aspects of Computer Science, pp. 294-305, 1993.
18. A. Czumaj, "Very Fast Approximation of the Matrix Chain Product Problem," J. Algorithms, vol. 21, no. 1, pp. 71-79, 1996.
19. P. Ramanan, "An Efficient Parallel Algorithm for the Matrix Chain Product Problem," SIAM J. Computing, vol. 25, pp. 874-893, Aug. 1996.
20. V. Strassen, "Gaussian Elimination Is Not Optimal," Numerical Math., vol. 13, pp. 354-356, 1969.
21. G.H. Golub and C.F.V. Loan, Matrix Computations, second ed., Baltimore: Johns Hopkins Univ. Press, 1989.
22. N.-K. Tsao, "Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product," IEEE Trans. Computers, vol. 30, no. 10, pp. 758-771, Oct. 1981.
23. C. Puglisi, "Parallel Algorithms and Architectures for Matrix Multiplication," Computer Math. Applications, vol. 17, no. 12, pp. 1567-1572, 1989.
24. A. Gupta and V. Kumar, "Scalability of Parallel Algorithms for Matrix Multiplication," Proc. Int'l Conf. Parallel Processing, pp. 115-123, 1993.
25. R. Krishnamurti and E. Ma, "An Approximation Algorithm for Scheduling Tasks on Varying Partition Sizes in Partitionable Multiprocessor Systems," IEEE Trans. Computers, vol. 41, no. 12, pp. 1572-1579, Dec. 1992.
26. S.G. Akl, The Design and Analysis of Parallel Algorithms. Englewood Cliffs, N.J.: Prentice Hall, Inc., 1989.
27. V. Sarkar, Partitioning and Scheduling Parallel Programs for Multiprocessors. Cambridge, Mass.: MIT Press, 1989.
28. C.D. Polychronopoulos and U. Banerjee, "Speedup Bounds and Processor Allocation for Parallel Programs on Multiprocessors," Proc. Int'l Conf. Parallel Processing, pp. 961-968, 1986.
29. C.D. Polychronopoulos and U. Banerjee, "Processor Allocation for Horizontal and Vertical Parallelism and Related Speedup Bounds," IEEE Trans. Computers, vol. 36, no. 4, pp. 410-420, Apr. 1987.
30. A. Schoor, "Fast Algorithm for Sparse Matrix Multiplication," Information Processing Letters, vol. 15, no. 2, pp. 87-89, 1982.
31. J. Takche, "Complexities of Special Matrix Multiplication Problems," Computer Math. Applications, vol. 15, no. 12, pp. 977-989, 1988.
32. J.W.H. Liu, "The Role of Elimination Trees in Sparse Factorization," SIAM J. Matrix Analysis and Applications, vol. 11, pp. 134-172, Jan. 1990.
33. J.W.H. Liu, "Equivalent Sparse Matrix Reordering by Elimination Tree Rotations," SIAM J. Scientific and Statistical Computing, vol. 9, pp. 424-444, May 1988.