article

Minimizing weighted flow time

Authors:

Kedar DhamdhereAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 3, Issue 4

Pages 39 - es

https://doi.org/10.1145/1290672.1290676

Published: 01 November 2007 Publication History

Abstract

We consider the problem of minimizing the total weighted flow time on a single machine with preemptions. We give an online algorithm that is O(k)-competitive for k weight classes. This implies an O(log W)-competitive algorithm, where W is the maximum to minimum ratio of weights. This algorithm also implies an O(log n + log P)-approximation ratio for the problem, where P is the ratio of the maximum to minimum job size and n is the number of jobs. We also consider the nonclairvoyant setting where the size of a job is unknown upon its arrival and becomes known to the scheduler only when the job meets its service requirement. We consider the resource augmentation model, and give a (1 + ε)-speed, (1 +1/ε)-competitive online algorithm.

References

[1]

Afrati, F., Bampis, E., Chekuri, C., Karger, D., Kenyon, C., Khanna, S., Millis, I., Queyranne, M., Skutella, M., Stein, C., and Sviridenko, M. 1999. Approximation schemes for minimizing average weighted completion time with release dates. In Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS), 32--43.

Digital Library

[2]

Avrahami, N., and Azar, Y. 2003. Minimizing total flow time and completion time with immediate dispacthing. In Proceedings of 15th ACM Annual Symposium on Paralllelism Alogrithms and Architectures (SPAA), 11--18.

Digital Library

[3]

Awerbuch, B., Azar, Y., Leonardi, S., and Regev, O. 1999. Minimizing the flow time without migration. In Proceedings of the ACM Symposium on Theory of Computing, 198--205.

Digital Library

[4]

Bansal, N. 2005. Minimizing flow time on a constant number of machines with preemption. Oper. Res. Lett. 33, 267--273.

Digital Library

[5]

Bansal, N., Dhamdhere, K., Konemann, J., and Sinha, A. 2003. Non-Clairvoyant scheduling for minimizing mean slowdown. In Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS), 260--270.

Digital Library

[6]

Bansal, N., and Pruhs, K. 2003. Server scheduling in the l<sub>p</sub> norm: A rising tide lifts all boats. In Proceedings of the ACM Symposium on Theory of Computing (STOC), 242--250.

Digital Library

[7]

Bansal, N., and Pruhs, K. 2004. Server scheduling in the weighted &ell;<sub>p</sub> norm. In Proceedings of the Latin American Symposium on Theoretical Informatics (LATIN), 434--443.

[8]

Becchetti, L., and Leonardi, S. 2004. Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines. J. ACM 51, 517--539.

Digital Library

[9]

Becchetti, L., Leonardi, S., and Muthukrishnan, S. 2000. Scheduling to minimize average stretch without migration. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 548--557.

Digital Library

[10]

Becchetti, L., Leonardi, S., Spaccamela, A. M., and Pruhs, K. 2001. Online weighted flow time and deadline scheduling. In Proceedings of the International Workshop on Randomination and Approximation Techniques (RANDOM-APPROX), 36--47.

Digital Library

[11]

Bender, M., Chakrabarti, S., and Muthukrishnan, S. 1998. Flow and stretch metrics for scheduling continuous job streams. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 270--279.

Digital Library

[12]

Bender, M., Muthukrishnan, S., and Rajaraman, R. 2002. Improved algorithms for stretch scheduling. In Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA).

Digital Library

[13]

Chekuri, C., Goel, A., Khanna, S., and Kumar, A. 2004. Multi-Processor scheduling to minimize flow time with epsilon resource augmentation. In Proceedings of the ACM Symposium on Theory of Computing (STOC), 363--372.

Digital Library

[14]

Chekuri, C., and Khanna, S. 2002. Approximation schemes for preemptive weighted flow time. In Proceedings of the ACM Symposium on Theory of Computing (STOC), 297--305.

Digital Library

[15]

Chekuri, C., Khanna, S., and Zhu, A. 2001. Algorithms for weighted flow time. In Proceedings of the ACM Symposium on Theory of Computing (STOC), 84--93.

Digital Library

[16]

Chekuri, C., Motwani, R., Natarajan, B., and Stein, C. 1997. Approximation techniques for average completion time scheduling. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 609-- 618.

Digital Library

[17]

Hall, L. A., Schulz, A. S., Shmoys, D. B., and Wein, J. 1997. Scheduling to minimize average completion time: Offline and online algorithms. Math. Oper. Res. 22, 513--544.

Digital Library

[18]

Kalyanasundaram, B., and Pruhs, K. 2000. Speed is as powerful as clairvoyance. J. ACM 47, 4, 617--643.

Digital Library

[19]

Kalyanasundaram, B., and Pruhs, K. 2003. Minimizing flow time nonclairvoyantly. J. ACM 50, 551--567.

Digital Library

[20]

Kellerer, H., Tautenhahn, T., and Woeginger, G. J. 1996. Approximability and nonapproximability results for minimizing total flow time on a single machine. In Proceedings of the ACM Symposium on Theory of Computing (STOC), 418--426.

Digital Library

[21]

Lenstra, J., Kan, A., and Brucker, P. 1977. Complexity of machine scheduling problems. Ann. Discrete Math. 1, 343--362.

[22]

Leonardi, S., and Raz, D. 1997. Approximating total flow time on parallel machines. In Proceedings of the ACM Symposium on Theory of Computing (STOC), 110--119.

Digital Library

[23]

Motwani, R., Phillips, S., and Torng, E. 1994. Nonclairvoyant scheduling. Theor. Comput. Sci. 130, 1, 17--47.

Digital Library

[24]

Muthukrishnan, S., Rajaraman, R., Shaheen, A., and Gehrke, J. 1999. Online scheduling to minimize average stretch. In Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS), 433--442.

Digital Library

[25]

Phillips, C. A., Stein, C., Torng, E., and Wein, J. 1997. Optimal time-critical scheduling via resource augmentation. In Proceedings of the ACM Symposium on Theory of Computing (STOC), 140--149.

Digital Library

[26]

Pruhs, K., Sgall, J., and Torng, E. 2004. Online scheduling. In Handbook of Scheduling: Algorithms, Models, and Performance Analysis. Ratan, FL, Chap. 35 CRC Press.

[27]

Schrage, L. 1968. A proof of the optimality of the shortest processing remaining time discipline. Oper. Res. 16, 678--690.

[28]

Smith, W. 1956. Various optimizers for single-stage production. Naval Res. Logistics Quart. 3, 59--66.

Cited By

Ben Mokhtar SCanon LDugois AMarchal LRivière E(2024)A scheduling framework for distributed key-value stores and its application to tail latency minimizationJournal of Scheduling10.1007/s10951-023-00803-827:2(183-202)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s10951-023-00803-8
Jäger SSagnol GSchmidt genannt Waldschmidt DWarode P(2024)Competitive kill-and-restart and preemptive strategies for non-clairvoyant schedulingMathematical Programming10.1007/s10107-024-02118-8Online publication date: 22-Jul-2024
https://doi.org/10.1007/s10107-024-02118-8
Jalota DPaccagnan DSchiffer MPavone M(2023)Online Routing Over Parallel NetworksINFORMS Journal on Computing10.1287/ijoc.2023.127535:3(560-577)Online publication date: 1-May-2023
https://dl.acm.org/doi/10.1287/ijoc.2023.1275
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Index Terms

Minimizing weighted flow time
1. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Scheduling algorithms
    2. Online algorithms
      1. Online learning algorithms
        Scheduling algorithms
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Reinforcement learning
        Sequential decision making

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 3, Issue 4

November 2007

293 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1290672

Issue’s Table of Contents

Copyright © 2007 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 01 November 2007

Published in TALG Volume 3, Issue 4

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Cited By

Ben Mokhtar SCanon LDugois AMarchal LRivière E(2024)A scheduling framework for distributed key-value stores and its application to tail latency minimizationJournal of Scheduling10.1007/s10951-023-00803-827:2(183-202)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s10951-023-00803-8
Jäger SSagnol GSchmidt genannt Waldschmidt DWarode P(2024)Competitive kill-and-restart and preemptive strategies for non-clairvoyant schedulingMathematical Programming10.1007/s10107-024-02118-8Online publication date: 22-Jul-2024
https://doi.org/10.1007/s10107-024-02118-8
Jalota DPaccagnan DSchiffer MPavone M(2023)Online Routing Over Parallel NetworksINFORMS Journal on Computing10.1287/ijoc.2023.127535:3(560-577)Online publication date: 1-May-2023
https://dl.acm.org/doi/10.1287/ijoc.2023.1275
Armbruster ARohwedder LWiese ASaha BServedio R(2023)A PTAS for Minimizing Weighted Flow Time on a Single MachineProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585146(1335-1344)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585146
Györgyi PKis TTamási TBékési J(2022)Joint replenishment meets schedulingJournal of Scheduling10.1007/s10951-022-00768-026:1(77-94)Online publication date: 8-Dec-2022
https://dl.acm.org/doi/10.1007/s10951-022-00768-0
Rohwedder LWiese AKhuller SVassilevska Williams V(2021)A (2 + ε)-approximation algorithm for preemptive weighted flow time on a single machineProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3406325.3451075(1042-1055)Online publication date: 15-Jun-2021
https://dl.acm.org/doi/10.1145/3406325.3451075
Azar YLeonardi STouitou NKhuller SVassilevska Williams V(2021)Flow time scheduling with uncertain processing timeProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3406325.3451023(1070-1080)Online publication date: 15-Jun-2021
https://dl.acm.org/doi/10.1145/3406325.3451023
Batra JGarg NKumar A(2020)Constant Factor Approximation Algorithm for Weighted Flow-Time on a Single Machine in PseudoPolynomial TimeSIAM Journal on Computing10.1137/19M124451252:6(FOCS18-158-FOCS18-188)Online publication date: 29-Sep-2020
https://doi.org/10.1137/19M1244512
Im SMoseley B(2020)Fair Scheduling via Iterative Quasi-Uniform SamplingSIAM Journal on Computing10.1137/18M120245149:3(658-680)Online publication date: 29-Jun-2020
https://doi.org/10.1137/18M1202451
Feige UKulkarni JLi SChan T(2019)A polynomial time constant approximation for minimizing total weighted flow-timeProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310531(1585-1595)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.5555/3310435.3310531
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