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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 $$1 + \frac{{N_m - 1}}{{N_m }}\frac{{r_m }}{3}and1 + \frac{{r_m }}{3}whereN_m = \frac{3}{{\sqrt e }}\left( {\frac{3}{2}} \right)^m - 2.$$
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 13, 2005
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