Theoretical Computer Science - Special issue on dynamic and on-line algorithms
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
Minimizing the flow time without migration
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
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
Improved algorithms for stretch scheduling
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Minimizing total flow time and total completion time with immediate dispatching
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Server scheduling in the Lp norm: a rising tide lifts all boat
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Online Scheduling to Minimize Average Stretch
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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
Competitive online scheduling for server systems
ACM SIGMETRICS Performance Evaluation Review
ACM Transactions on Algorithms (TALG)
Minimizing flow time on a constant number of machines with preemption
Operations Research Letters
Speed scaling with an arbitrary power function
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Non-clairvoyant scheduling for weighted flow time and energy on speed bounded processors
CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
Scalably scheduling power-heterogeneous processors
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Non-clairvoyant speed scaling for weighted flow time
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
An online scalable algorithm for minimizing lk-norms of weighted flow time on unrelated machines
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Speed Scaling with an Arbitrary Power Function
ACM Transactions on Algorithms (TALG)
Competitive online algorithms for multiple-machine power management and weighted flow time
CATS '13 Proceedings of the Nineteenth Computing: The Australasian Theory Symposium - Volume 141
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We consider the classic online scheduling problem of minimizing the total weighted flow time on a single machine with preemptions. Here, each job j has an arbitrary arrival time rj, weight wj and size pj, and given a schedule its flow time is defined as the duration of time since its arrival until it completes its service requirement. The first non-trivial algorithms with poly-logarithmic competitive ratio for this problem were obtained relatively recently, and it was widely believed that the problem admits a constant factor competitive algorithm. In this paper, we show an ω(1) lower bound on the competitive ratio of any deterministic online algorithm. Our result is based on a gap amplification technique for online algorithms. Starting with a trivial lower bound of 1, we give a procedure to improve the lower bound sequentially, while ensuring at each step that the size of the instance increases relatively modestly.