Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Approximation techniques for average completion time scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Speed is as powerful as clairvoyance
Journal of the ACM (JACM)
Algorithms for minimizing weighted flow time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation schemes for preemptive weighted flow time
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Speed is more powerful than clairvoyance
Nordic Journal of Computing
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Non-clairvoyant Scheduling for Minimizing Mean Slowdown
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Server scheduling in the Lp norm: a rising tide lifts all boat
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Multi-processor scheduling to minimize flow time with ε resource augmentation
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Competitive online scheduling for server systems
ACM SIGMETRICS Performance Evaluation Review
Approximating total flow time on parallel machines
Journal of Computer and System Sciences
Greedy multiprocessor server scheduling
Operations Research Letters
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We consider the problem of minimizing weighted flow time on a single machine in the preemptive setting. Our main result is an O(log W) competitive online algorithm where the maximum to the minimum ratio of weights is W. More generally our algorithm achieves a competitive ratio of k if there are k weight classes. This gives the first O(1)-competitive algorithm for constant k. No O(1) competitive algorithm was known previously even for the special case of k = 2. These results settle a question posed by Chekuri et al [5] about the existence of a "truly" online algorithm with a non-trivial competitive ratio. We also give a "semi-online" algorithm with competitive ratio O(log n + log P), where P is ratio of the maximum to minimum job size. Our second result deals with the non-clairvoyant setting where the job sizes are unknown (but the weight of the jobs are known). We consider the resource augmentation model, and give a non-clairvoyant online algorithm, which if allowed a (1 + ε) speed-up, is (1 + l/ε) competitive against an optimal offline, clairvoyant algorithm.