Speed is as powerful as clairvoyance
Journal of the ACM (JACM)
Theoretical Computer Science - Selected papers in honor of Manuel Blum
Algorithms for minimizing weighted flow time
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Minimizing the Flow Time Without Migration
SIAM Journal on Computing
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
Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines
Journal of the ACM (JACM)
Online Scheduling to Minimize Average Stretch
SIAM Journal on Computing
Approximating total flow time on parallel machines
Journal of Computer and System Sciences
SRPT optimally utilizes faster machines to minimize flow time
ACM Transactions on Algorithms (TALG)
Scheduling heterogeneous processors isn't as easy as you think
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
Nonclairvoyant sleep management and flow-time scheduling on multiple processors
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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Due to its optimality on a single machine for the problem of minimizing average flow time, Shortest-Remaining-Processing-Time (SRPT) appears to be the most natural algorithm to consider for the problem of minimizing average flow time on multiple identical machines. It is known that SRPT achieves the best possible competitive ratio on multiple machines up to a constant factor. Using resource augmentation, SRPT is known to achieve total flow time at most that of the optimal solution when given machines of speed 2 − 1/m. Further, it is known that SRPT's competitive ratio improves as the speed increases; SRPT is s-speed 1/s-competitive when s ≥ 2--1/m. However, a gap has persisted in our understanding of SRPT. Before this work, the performance of SRPT was not known when SRPT is given (1 + ε)-speed when 0 m, even though it has been thought that SRPT is (1 + ε)-speed O(1)-competitive for over a decade. Resolving this question was suggested in Open Problem 2.9 from the survey "Online Scheduling" by Pruhs, Sgall, and Torng [PST04], and we answer the question in this paper. We show that SRPT is scalable on m identical machines. That is, we show SRPT is (1 + ε)-speed O(1/ε)-competitive for ε 0. We complement this by showing that SRPT is (1 + ε)-speed O(1/ε2)-competitive for the objective of minimizing the lk-norms of flow time on m identical machines. Both of our results rely on new potential functions that capture the structure of SRPT. Our results, combined with previous work, show that SRPT is the best possible online algorithm in essentially every aspect when migration is permissible.