# Parametric bounds for LPT scheduling on uniform processors

Parametric bounds for LPT scheduling on uniform processors 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 $$1 + \frac{{N_m - 1}}{{N_m }}\frac{{r_m }}{3}and1 + \frac{{r_m }}{3}whereN_m = \frac{3}{{\sqrt e }}\left( {\frac{3}{2}} \right)^m - 2.$$ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Parametric bounds for LPT scheduling on uniform processors

, Volume 7 (1) – Jul 13, 2005
7 pages

/lp/springer-journals/parametric-bounds-for-lpt-scheduling-on-uniform-processors-612TwXJ004
Publisher
Springer Journals
Copyright © 1991 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02080204
Publisher site
See Article on Publisher Site

### 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 $$1 + \frac{{N_m - 1}}{{N_m }}\frac{{r_m }}{3}and1 + \frac{{r_m }}{3}whereN_m = \frac{3}{{\sqrt e }}\left( {\frac{3}{2}} \right)^m - 2.$$

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

### References

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