A lower bound for randomized on-line multiprocessor scheduling
Information Processing Letters
A Level Algorithm for Preemptive Scheduling
Journal of the ACM (JACM)
Preemptive Scheduling of Uniform Processor Systems
Journal of the ACM (JACM)
Theoretical Computer Science
Approximation Schemes for Covering and Scheduling on Related Machines
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Semi on-line algorithms for the partition problem
Operations Research Letters
A polynomial-time approximation scheme for maximizing the minimum machine completion time
Operations Research Letters
Ordinal algorithms for parallel machine scheduling
Operations Research Letters
Preemptive on-line scheduling for two uniform processors
Operations Research Letters
An optimal algorithm for preemptive on-line scheduling
Operations Research Letters
Semi-online scheduling with decreasing job sizes
Operations Research Letters
Semi-on-line scheduling with ordinal data on two uniform machines
Operations Research Letters
Semi-on-line problems on two identical machines with combined partial information
Operations Research Letters
Optimal preemptive semi-online scheduling to minimize makespan on two related machines
Operations Research Letters
Approximation schemes for scheduling and covering on unrelated machines
Theoretical Computer Science
Semi-online machine covering for two uniform machines
Theoretical Computer Science
Preemptive semi-online scheduling on parallel machines with inexact partial information
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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In this paper, we consider the semi-online preemptive scheduling problem with decreasing job sizes on two uniform machines. Our goal is to maximize the continuous period of time (starting from time zero) when both machines are busy, which is equivalent to maximizing the minimum machine completion time if idle time is not introduced before all the jobs are completed. We design optimal deterministic semi-online algorithms for every machine speed ratio s ∈ [1, ∞), and show that idle time is required during the assignment procedure of algorithms for any s √6/2. The competitive ratios of the algorithms match the randomized lower bound for every 1 ≤ s ≤ 3. The problem of whether randomization still does not help for the discussed preemptive scheduling problem remains open.