A lower bound for randomized on-line scheduling algorithms
Information Processing Letters
A simple semi on-line algorithm for P2//Cmax with a buffer
Information Processing Letters
A lower bound for randomized on-line multiprocessor scheduling
Information Processing Letters
A Level Algorithm for Preemptive Scheduling
Journal of the ACM (JACM)
Preemptive multiprocessor scheduling with rejection
Theoretical Computer Science
Developments from a June 1996 seminar on Online algorithms: the state of the art
Study on Parallel Machine Scheduling Problem with Buffer
IMSCCS '07 Proceedings of the Second International Multi-Symposiums on Computer and Computational Sciences
The Power of Reordering for Online Minimum Makespan Scheduling
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Semi-Online Preemptive Scheduling: One Algorithm for All Variants
Theory of Computing Systems
A lower bound for on-line scheduling on uniformly related machines
Operations Research Letters
Semi on-line algorithms for the partition problem
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
Optimal preemptive on-line scheduling on uniform processors with non-decreasing speed ratios
Operations Research Letters
Optimal preemptive semi-online scheduling to minimize makespan on two related machines
Operations Research Letters
Robust algorithms for preemptive scheduling
ESA'11 Proceedings of the 19th European conference on Algorithms
Online minimum makespan scheduling with a buffer
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
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We consider online preemptive scheduling of jobs, arriving one by one, on $m$ identical parallel machines. A buffer of a fixed size $K0$, which assists in partial reordering of the input, is available to be used for the storage of at most $K$ unscheduled jobs. We study the effect of using a fixed-size buffer (of an arbitrary size) on the supremum competitive ratio over all numbers of machines (the overall competitive ratio), as well as the effect on the competitive ratio as a function of $m$. We find a tight bound on the competitive ratio for any $m$. This bound is $\frac{4}{3}$ for even values of $m$ and slightly lower for odd values of $m$. We show that a buffer of size $\Theta(m)$ is sufficient to achieve this bound, but using $K=o(m)$ does not reduce the best overall competitive ratio that is known for the case without reordering, $\frac{e}{e-1}$. We further consider the semionline variant where jobs arrive sorted by nonincreasing processing time requirements. In this case it turns out to be possible to achieve a competitive ratio of 1. In addition, we find tight bounds as a function of the buffer size and the number of machines for this semionline variant. Related results for nonpreemptive scheduling were recently obtained by Englert, Özmen, and Westermann.