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
Algorithms for minimizing weighted flow time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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
Speed is as powerful as clairvoyance [scheduling problems]
FOCS '95 Proceedings of the 36th 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
Minimizing Average Flow-time: Upper and Lower Bounds
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Speed scaling with an arbitrary power function
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Proceedings of the forty-first annual ACM symposium on Theory of computing
Scalably scheduling power-heterogeneous processors
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Speed Scaling for Weighted Flow Time
SIAM Journal on Computing
Better algorithms for minimizing average flow-time on related machines
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
The complexity of scheduling for p-norms of flow and stretch
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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
Minimizing maximum (weighted) flow-time on related and unrelated machines
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Recent advances for a classical scheduling problem
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Coordination mechanisms from (almost) all scheduling policies
Proceedings of the 5th conference on Innovations in theoretical computer science
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We propose a general dual-fitting technique for analyzing online scheduling algorithms in the unrelated machines setting where the objective function involves weighted flow-time, and we allow the machines of the on-line algorithm to have (1 + ε)-extra speed than the offline optimum (the so-called speed augmentation model). Typically, such algorithms are analyzed using non-trivial potential functions which yield little insight into the proof technique. We propose that one can often analyze such algorithms by looking at the dual (or Lagrangian dual) of the linear (or convex) program for the corresponding scheduling problem, and finding a feasible dual solution as the on-line algorithm proceeds. As representative cases, we get the following results: • For the problem of minimizing weighted flow-time, we give an O (1/ε)-competitive greedy algorithm. This is an improvement by a factor of 1/ε on the competitive ratio of the greedy algorithm of Chadha-Garg-Kumar-Muralidhara. • For the problem of minimizing weighted lk norm of flow-time, we show that a greedy algorithm gives an O (1/ε)-competitive ratio. This marginally improves the result of Im and Moseley. • For the problem of minimizing weighted flow-time plus energy, and when the energy function f(s) is equal to sγ, γ 1, we show that a natural greedy algorithm is O(γ2)-competitive. Prior to our work, such a result was known for the related machines setting only (Gupta-Krishnaswamy-Pruhs).