Multiprocessor Online Scheduling of Hard-Real-Time Tasks
IEEE Transactions on Software Engineering
Approximability and nonapproximability results for minimizing total flow time on a single machine
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Approximating total flow time on parallel machines
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Optimal time-critical scheduling via resource augmentation (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Online computation and competitive analysis
Online computation and competitive analysis
Scheduling data transfers in a network and the set scheduling problem
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Minimizing the flow time without migration
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Optimal On-Line Algorithms for Single-Machine Scheduling
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Speed is as powerful as clairvoyance [scheduling problems]
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
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We study the problem of scheduling n jobs that arrive over time. We consider a non-preemptive setting on a single machine. The goal is to minimize the total flow time.We use extra resource competitive analysis: an optimal off-line algorithm which schedules jobs on a single machine is compared to a more powerful on-line algorithm that has l machines. We design an algorithm of competitive ratio O(min(Δ1/l, n1/l)), where Δ is the maximum ratio between two job sizes, and provide a lower bound which shows that the algorithm is optimal up to a constant factor for any constant l. The algorithm works for a hard version of the problem where the sizes of the smallest and the largest jobs are not known in advance, only Δ is known. This gives a trade-off between the resource augmentation and the competitive ratio. We also consider scheduling on parallel identical machines. In this case the optimal off-line algorithm has m machines and the on-line algorithm has lm machines. We give a lower bound for this case. Next, we give lower bounds for algorithms using resource augmentation on the speed. Finally, we consider scheduling with hard deadlines.