Abstract
The nonpreemptive assignment of independent tasks to a system ofm uniform processors is examined with the objective of minimizing the makespan. Usingτ m , the ratio of the fastest speed to the slowest speed of the system, as a parameter, we assess the performance of LPT (largest processing time) schedule with respect to optimal schedules. It is shown that the worst-case bound for the ratio of the two schedule lengths is between\(1 + \frac{{N_m - 1}}{{N_m }}\frac{{r_m }}{3}and1 + \frac{{r_m }}{3}whereN_m = \frac{3}{{\sqrt e }}\left( {\frac{3}{2}} \right)^m - 2.\)
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Dobson, Scheduling Independent Tasks on Uniform Processors,SIAM J. Comput.,13 (1984), 705–716.
D. K. Friesen, Tighter Bounds for LPT Scheduling on Uniform Processors,SIAM J. Comput.,16 (1987), 554–560.
M. R. Garey and D. S. Johnson, Computers and Intractability, a Guide to the Theory of NP-Completeness, Freeman, San Francisco (1979).
T. Gonzalez, O. H. Ibarra and S. Sahni, Bounds for LPT Schedules on Uniform Processors,SIAM J. Comput.,6 (1977), 155–166.
R. L. Graham, Bounds on Multiprocessor Timing Anomalies,SIAM J. Applied Mathematics,17 (1969), 416–429.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chen, B. Parametric bounds for LPT scheduling on uniform processors. Acta Mathematicae Applicatae Sinica 7, 67–73 (1991). https://doi.org/10.1007/BF02080204
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02080204