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K.K. Jain, V. Rajaraman, "Lower and Upper Bounds on Time for Multiprocessor Optimal Schedules," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 8, pp. 879886, August, 1994.  
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@article{ 10.1109/71.298216, author = {K.K. Jain and V. Rajaraman}, title = {Lower and Upper Bounds on Time for Multiprocessor Optimal Schedules}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {5}, number = {8}, issn = {10459219}, year = {1994}, pages = {879886}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.298216}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Lower and Upper Bounds on Time for Multiprocessor Optimal Schedules IS  8 SN  10459219 SP879 EP886 EPD  879886 A1  K.K. Jain, A1  V. Rajaraman, PY  1994 KW  Index Termsparallel algorithms; scheduling; directed graphs; minimisation; lower time bound; upper time bound; multiprocessor optimal schedules; minimum processing time; directed acyclic task graph; worst case behavior; minimum processor number; randomly generated dense task graphs; parallel processing; performance evaluation VL  5 JA  IEEE Transactions on Parallel and Distributed Systems ER   
The lower and upper bounds on the minimum time needed to process a given directedacyclic task graph for a given number of processors are derived. It is proved that theproposed lower bound on time is not only sharper than the previously known values butalso easier to calculate. The upper bound on time, which is useful in determining theworst case behavior of a given task graph, is presented. The lower and upper bounds onthe minimum number of processors required to process a given task graph in the minimum possible time are also derived. It is seen with a number of randomly generated dense task graphs that the lower and upper bounds we derive are equal, thus giving the optimal time for scheduling directed acyclic task graphs on a given set of processors.
[1] T. C. Hu, "Parallel sequencing and assembly line problems,"Oper. Res., vol. 9, pp. 841848, Nov. 1961.
[2] C. V. Ramamoorthy, K. M. Chandy and M. J. Gonzalez, "Optimal scheduling strategies in a multiprocessor system,"IEEE Trans. Comput., vol. C21, no. 2, pp. 137146, Feb. 1972.
[3] E. B. Fernandez and B. Bussell, "Bounds on the number of processors and time for multiprocessors optimal schedules,"IEEE Trans. Comput., vol. C22, no. 8, pp. 745751, Aug. 1973.
[4] E. G. Coffmanet al., Eds.,Computer and JobShop Scheduling Theory. New York: Wiley, 1976.
[5] R. L. Graham, "Bounds on multiprocessing timing anomalies,"SIAM J. Appl. Maths., vol. 17, pp. 416429, 1969.
[6] D. Helmbold and R. Mayr, "Two processor scheduling is in NC,"SIAM J. Computing, vol. 16, no. 4, pp. 747759, Aug. 1987.
[7] E. Coffman and R. Graham, "Optimal scheduling for two processor systems,"Acta Informatica, vol. 1, pp. 200213, 1972.
[8] T. Kawaguchi and S. Kyan, "Worst case bound on an LRF schedule for the mean weighted flowtime problem,"SIAM J. Computing, vol. 15, no. 4, pp. 11191129, Nov. 1986.
[9] D. Dolev and M. Warmuth, "Scheduling flat graphs,"SIAM J. Computing, vol. 14, no. 3, pp. 638657, Aug. 1985.
[10] D. Dolev and M. Warmuth, "Scheduling precedence graphs of bounded height,"J. Algorithms, vol. 5, pp. 4859, 1984.
[11] H. N. Gabow, "An almost linear algorithm for two processor scheduling,"J. ACM, vol. 29, no. 3, pp. 766780, 1982.
[12] C. Siva Ram Murthy and V. Rajaraman, "Task assignment in a multiprocessor system,"Microprocessing and Microprogramming. vol. 26, pp. 6371, 1989.
[13] J. D. Ullman, "NPcomplete scheduling problems,"J. Comput. Sys. Sci., vol. 10, pp. 384393, 1975.
[14] D. J. Kucket al., "Measurements of parallelism in ordinary Fortran program,"Comput., vol. 7, no. 1, pp. 3746, 1974.
[15] B. Jereb and L. Pipan, "Measuring parallelism in algorithms,"Microprocessing and Microprogramming: Euromicro J., vol. 34, pp. 4952, 1992.
[16] K. K. Jain and V. Rajaraman, "Parallelism measures of task graphs on multiprocessors,"Microprocessing and Microprogramming, to appear.
[17] K. Soet al., "A speedup analyzer for parallel programs," inProc. ICPP, 1987, pp. 653661.
[18] B. P. Lester, "A system for computing the speedup of parallel programs," inProc. ICPP, 1986, pp. 145152.
[19] C. Polychronopoulos and U. Banerjee, "Speedup bounds and processors allocation for parallel programs on multiprocessors," inProc. ICPP, 1986, pp. 961968.
[20] X.H. Sun and L.M. Ni, "Another View of Parallel Speedup,"Proc. Supercomputing '90, IEEE Computer Soc. Press, Los Alamitos, Calif., 1990, pp. 324333.
[21] N. L. Soong, "Performance bounds for a certain class of parallel processing," inProc. ICPP, 1979, p. 115.
[22] D. L. Eager, J. Zahorjan, and E. D. Lazowska, "Speedup versus efficiency in parallel systems,"IEEE Trans. Comput., vol. 38, pp. 408422, March 1989.