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
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
Speed is as powerful as clairvoyance
Journal of the ACM (JACM)
Optimal On-Line Algorithms for Single-Machine Scheduling
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
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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 @? machines. We design an algorithm of competitive ratio 1+2min(@D^1^/^@?,n^1^/^@?), where @D 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 @?. 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 @D and n are 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 @?m 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, and scheduling so as to minimize the total completion time.