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Minimizing average flow time on related machines

Published: 21 May 2006 Publication History

Abstract

We give the first on-line poly-logarithmic competitve algorithm for minimizing average flow time with preemption on related machines, i.e., when machines can have different speeds. This also yields the first poly-logarithmic polynomial time approximation algorithm for this problem.More specifically, we give an O(log2 P • log S)-competitive algorithm, where P is the ratio of the biggest and the smallest processing time of a job, and S is the ratio of the highest and the smallest speed of a machine. Our algorithm also has the nice property that it is non-migratory. The scheduling algorithm is based on the concept of making jobs wait for a long enough time before scheduling them on slow machines.

References

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Baruch Awerbuch, Yossi Azar, Stefano Leonardi, and Oded Regev. Minimizing the flow time without migration. In ACM Symposium on Theory of Computing, pages 198--205, 1999.
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N. Bansal and K. Pruhs. Server scheduling in the l p norm: A rising tide lifts all boats. In ACM Symposium on Theory of Computing, pages 242--250, 2003.
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Luca Becchetti, Stefano Leonardi, Alberto Marchetti-Spaccamela, and Kirk R. Pruhs. Online weighted flow time and deadline scheduling. Lecture Notes in Computer Science, 2129:36--47, 2001.
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C. Chekuri, S. Khanna, and A. Zhu. Algorithms for weighted flow time. In ACM Symposium on Theory of Computing, pages 84--93. ACM, 2001.
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Chandra Chekuri, Ashish Goel, Sanjeev Khanna, and Amit Kumar. Multi-processor scheduling to minimize flow time with epsilon resource augmentation. In ACM Symposium on Theory of Computing, pages 363--372, 2004.
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Bala Kalyanasundaram and Kirk Pruhs. Speed is as powerful as clairvoyance. In IEEE Symposium on Foundations of Computer Science, pages 214--221, 1995.
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Hans Kellerer, Thomas Tautenhahn, and Gerhard J. Woeginger. Approximability and nonapproximability results for minimizing total flow time on a single machine. In ACM Symposium on Theory of Cmputing, pages 418--426, 1996.
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Stefano Leonardi and Danny Raz. Approximating total flow time on parallel machines. In ACM Symposium on Theory of Computing, pages 110--119, 1997.
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Cited By

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  • (2024)Scheduling Multi-Server Jobs is Not EasyProceedings of the Twenty-fifth International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing10.1145/3641512.3686374(171-180)Online publication date: 14-Oct-2024
  • (2023)Online Approximation Scheme for Scheduling Heterogeneous Utility Jobs in Edge ComputingIEEE/ACM Transactions on Networking10.1109/TNET.2022.319338131:1(352-365)Online publication date: Feb-2023
  • (2020)Fair Scheduling via Iterative Quasi-Uniform SamplingSIAM Journal on Computing10.1137/18M120245149:3(658-680)Online publication date: 1-Jan-2020
  • Show More Cited By

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cover image ACM Conferences
STOC '06: Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing
May 2006
786 pages
ISBN:1595931341
DOI:10.1145/1132516
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

New York, NY, United States

Publication History

Published: 21 May 2006

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Author Tags

  1. approximation algorithms
  2. competitive ratio
  3. flow-time
  4. scheduling

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STOC06
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STOC06: Symposium on Theory of Computing
May 21 - 23, 2006
WA, Seattle, USA

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

View all
  • (2024)Scheduling Multi-Server Jobs is Not EasyProceedings of the Twenty-fifth International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile Computing10.1145/3641512.3686374(171-180)Online publication date: 14-Oct-2024
  • (2023)Online Approximation Scheme for Scheduling Heterogeneous Utility Jobs in Edge ComputingIEEE/ACM Transactions on Networking10.1109/TNET.2022.319338131:1(352-365)Online publication date: Feb-2023
  • (2020)Fair Scheduling via Iterative Quasi-Uniform SamplingSIAM Journal on Computing10.1137/18M120245149:3(658-680)Online publication date: 1-Jan-2020
  • (2018)Improved Online Algorithm for Weighted Flow Time2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2018.00048(427-437)Online publication date: Oct-2018
  • (2017)Fair scheduling via iterative quasi-uniform samplingProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039857(2601-2615)Online publication date: 16-Jan-2017
  • (2016)Minimum Flow TimeEncyclopedia of Algorithms10.1007/978-1-4939-2864-4_235(1312-1315)Online publication date: 22-Apr-2016
  • (2015)Minimizing Flow-Time on Unrelated MachinesProceedings of the forty-seventh annual ACM symposium on Theory of Computing10.1145/2746539.2746601(851-860)Online publication date: 14-Jun-2015
  • (2014)Minimum Flow TimeEncyclopedia of Algorithms10.1007/978-3-642-27848-8_235-2(1-4)Online publication date: 29-Oct-2014
  • (2011)An online scalable algorithm for minimizing l-norms of weighted flow time on unrelated machinesProceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms10.5555/2133036.2133044(95-108)Online publication date: 23-Jan-2011
  • (2009)A competitive algorithm for minimizing weighted flow time on unrelatedmachines with speed augmentationProceedings of the forty-first annual ACM symposium on Theory of computing10.1145/1536414.1536506(679-684)Online publication date: 31-May-2009
  • Show More Cited By

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