A lower bound for randomized on-line scheduling algorithms
Information Processing Letters
The competitiveness of on-line assignments
Journal of Algorithms
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
A lower bound for randomized on-line multiprocessor scheduling
Information Processing Letters
On-line load balancing for related machines
Journal of Algorithms
Preemptive multiprocessor scheduling with rejection
Theoretical Computer Science
On-Line Load Balancing in a Hierarchical Server Topology
SIAM Journal on Computing
On-line algorithms for the channel assignment problem in cellular networks
Discrete Applied Mathematics
Preemptive online scheduling: optimal algorithms for all speeds
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Online and semi-online scheduling of two machines under a grade of service provision
Operations Research Letters
A lower bound for on-line scheduling on uniformly related machines
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
Optimal preemptive on-line scheduling on uniform processors with non-decreasing speed ratios
Operations Research Letters
Online and semi-online hierarchical scheduling for load balancing on uniform machines
Theoretical Computer Science
Optimal online algorithms on two hierarchical machines with resource augmentation
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Online scheduling on uniform machines with two hierarchies
Journal of Combinatorial Optimization
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We consider preemptive offline and online scheduling on identical machines and uniformly related machines in the hierarchical model, with the goal of minimizing the makespan. In this model, each job can be assigned to a subset of the machines which is a prefix of the machine set. We design optimal offline and online algorithms for two uniformly related machines, both when the machine of higher hierarchy is faster and when it is slower, as well as for the case of three identical machines. Specifically, for each one of the three variants, we give a simple formula to compute the makespan of an optimal schedule, provide a linear time offline algorithm which computes an optimal schedule and design an online algorithm of the best possible competitive ratio.