Preemptive Online Scheduling: Optimal Algorithms for All Speeds

Authors:
Tomáš Ebenlendr;Wojciech Jawor;Jiří Sgall
Affiliations:
Institute of Mathematics, AS CR, Žitná 25, 11567, Praha 1, Czech Republic;University of California, Department of Computer Science, 92521, Riverside, CA, USA;Institute of Mathematics, AS CR, Žitná 25, 11567, Praha 1, Czech Republic
Venue:
Algorithmica
Year:
2009

Citing 0
Cited 6

Optimal and online preemptive scheduling on uniformly related machines

Journal of Scheduling
Robust algorithms for preemptive scheduling

ESA'11 Proceedings of the 19th European conference on Algorithms
Preemptive Online Scheduling with Reordering

SIAM Journal on Discrete Mathematics
A lower bound on deterministic online algorithms for scheduling on related machines without preemption

WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Preemptive online scheduling with rejection of unit jobs on two uniformly related machines

Journal of Scheduling
Lower bounds for online makespan minimization on a small number of related machines

Journal of Scheduling

Quantified Score

Hi-index	0.03

Visualization

Abstract

Our main result is an optimal online algorithm for preemptive scheduling on uniformly related machines with the objective to minimize makespan. The algorithm is deterministic, yet it is optimal even among all randomized algorithms. In addition, it is optimal for any fixed combination of speeds of the machines, and thus our results subsume all the previous work on various special cases. Together with a new lower bound it follows that the overall competitive ratio of this optimal algorithm is between 2.054 and e≈2.718. We also give a complete analysis of the competitive ratio for three machines.