The competitiveness of on-line assignments
Journal of Algorithms
A simple semi on-line algorithm for P2//Cmax with a buffer
Information Processing Letters
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
Better Bounds for Online Scheduling
SIAM Journal on Computing
Generating adversaries for request-answer games
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On-line load balancing for related machines
Journal of Algorithms
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Optimal semi-online algorithms for machine covering
Theoretical Computer Science
An approximation algorithm for max-min fair allocation of indivisible goods
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The Power of Reordering for Online Minimum Makespan Scheduling
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
A note on semi-online machine covering
WAOA'05 Proceedings of the Third international conference on Approximation and Online 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
An optimal algorithm for preemptive on-line scheduling
Operations Research Letters
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We consider online scheduling so as to maximize the minimum load, using a reordering buffer which can store some of the jobs before they are assigned irrevocably to machines. For m identical machines, we show an upper bound of Hm-1 + 1 for a buffer of size m - 1. A competitive ratio below Hm is not possible with any finite buffer size, and it requires a buffer of size Ω(m) to get a ratio of O(logm). For uniformly related machines, we show that a buffer of size m+1 is sufficient to get an approximation ratio of m, which is best possible for any finite sized buffer. Finally, for the restricted assignment model, we show lower bounds identical to those of uniformly related machines, but using different constructions. In addition, we design an algorithm of approximation ratio O(m) which uses a finite sized buffer. We give tight bounds for two machines in all the three models. These results sharply contrast to the (previously known) results which can be achieved without the usage of a reordering buffer, where it is not possible to get a ratio below an approximation ratio of m already for identical machines, and it is impossible to obtain an algorithm of finite approximation ratio in the other two models, even for m = 2. Our results strengthen the previous conclusion that a reordering buffer is a powerful tool and it allows a significant decrease in the competitive ratio of online algorithms for scheduling problems. Another interesting aspect of our results is that our algorithm for identical machines imitates the behavior of the greedy algorithm on (a specific set of) related machines, whereas our algorithm for related machines completely ignores the speeds until the end, and then only uses the relative order of the speeds.