Power of Preemption on Uniform Parallel Machines

For a scheduling problem on parallel machines, the power of preemption is defined as the ratio of the makespan of an optimal non-preemptive schedule over the makespan of an optimal preemptive schedule. For m uniform parallel machines, we give the necessary and sufficient conditions under which the global bound of 2 − 1/m is tight. If the makespan of the optimal preemptive schedule is defined by the ratio of the total processing times of r < m longest jobs over the total speed of r fastest machines, we show that the tight bound on the power of preemption is 2− 1/min {r,m− r}. 1998 ACM Subject Classification F.2.2 Sequencing and Scheduling, G.2.1 Combinatorial Algorithms, G.1.6.Optimization