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Encyclopedia of Algorithms pp 806–809Cite as

Scheduling with Equipartition

2000; Edmonds

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Keywords and Synonyms

Round Robin and Equi‐partition are the same algorithm. Average Response time and Flow are basically the same measure.             

Problem Definition

The task is to schedule a set of n on-line jobs on p processors. The jobs are \( { J=\left\{J_1, \dots, J_n \right\} } \) where job J i has a release/arrival time r i and a sequence of phases \( \langle J_i^1, J_i^2, \dots, J_i^{q_i} \rangle \). Each phase is represented by \( { \langle w_i^q, \Gamma_i^q \rangle } \), where \( { w_i^q } \) denotes the amount of work and \( { \Gamma_i^q } \) is the speedup function specifying the rate \( { \Gamma_i^q (\beta) } \) at which this work is executed when given β processors.

A phase of a job is said to be fully parallelizable if its speedup function is \( { \Gamma(\beta) = \beta } \). It is said to be sequential if its speedup function is \( { \Gamma (\beta) = 1 } \).Footnote 1 A speedup function Γ is nondecreasing iff \( { \Gamma(\beta_1) \leq \Gamma(\beta_2) } \) whenever \( { \beta_1...

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Notes

  1. 1.

    Note that an odd feature of this definition is that a sequential job completes work at a rate of 1 even when absolutely no processors are allocated to it. This assumption makes things easier for the adversary and harder for any non‐clairvoyant algorithm. Hence, it only makes these results stronger.

  2. 2.

    A job phase with a nondecreasing speedup function executes no slower if it is allocated more processors.

  3. 3.

    A measure of how efficient a job utilizes its processors is \( { \Gamma(\beta) / \beta } \), which is the work completed by the job per time unit per processor. A sublinear speedup function is one whose efficiency does not increase with more processors. This is a reasonable assumption if in practice \( { \beta_1 } \) processors can simulate the execution of \( { \beta_2 } \) processors in a factor of at most \( { \beta_2/\beta_1 } \) more time.

  4. 4.

    \( { S^s(J) } \) is defined to be the scheduler with p processors of speed s. S s and S s are equivalent on fully parallelizable jobs and S s is s times faster than S s on sequential jobs.

Recommended Reading

  1. Edmonds, J.: Scheduling in the dark. Improved results: manuscript 2001. In: Theor. Comput. Sci. 235, 109–141 (2000). In: 31st Ann. ACM Symp. on Theory of Computing, 1999

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  2. Edmonds, J.: On the Competitiveness of AIMD-TCP within a General Network. In: LATIN, Latin American Theoretical Informatics, vol. 2976, pp. 577–588 (2004). Submitted to Journal Theoretical Computer Science and/or Lecture Notes in Computer Science

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  3. Edmonds, J., Chinn, D., Brecht, T., Deng, X.: Non‐clairvoyant Multiprocessor Scheduling of Jobs with Changing Execution Characteristics. In: 29th Ann. ACM Symp. on Theory of Computing, 1997, pp. 120–129. Submitted to SIAM J. Comput.

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  4. Edmonds, J., Datta, S., Dymond, P.: TCP is Competitive Against a Limited Adversary. In: SPAA, ACM Symp. of Parallelism in Algorithms and Achitectures, 2003, pp. 174–183

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  5. Edmonds, J., Pruhs, K.: Multicast pull scheduling: when fairness is fine. Algorithmica 36, 315–330 (2003)

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  6. Edmonds, J., Pruhs, K.: A maiden analysis of longest wait first. In: Proc. 15th Symp. on Discrete Algorithms (SODA)

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  7. Kalyanasundaram, B., Pruhs, K.: Minimizing flow time nonclairvoyantly. In: Proceedings of the 38th Symposium on Foundations of Computer Science, October 1997

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  8. Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. In: Proceedings of the 36th Symposium on Foundations of Computer Science, October 1995, pp. 214–221

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  9. Matsumoto: Competitive Analysis of the Round Robin Algorithm. in: 3rd International Symposium on Algorithms and Computation, 1992, pp. 71–77

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  10. Motwani, R., Phillips, S., Torng, E.: Non‐clairvoyant scheduling. Theor. Comput. Sci. 130 (Special Issue on Dynamic and On-Line Algorithms), 17–47 (1994). Preliminary Version in: Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithms, 1993, pp. 422–431

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  11. Robert, J., Schabanel, N.: Non‐Clairvoyant Batch Sets Scheduling: Fairness is Fair enough. Personal Correspondence (2007)

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Author information

Authors and Affiliations

  1. York University, Toronto, ON, Canada

    Jeff Edmonds

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  1. Jeff Edmonds
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Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Edmonds, J. (2008). Scheduling with Equipartition. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_357

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