Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Algorithms pp 531–533Cite as

Minimum Flow Time

1997; Leonardi, Raz

  • Reference work entry

  • 278 Accesses

Keywords and Synonyms

Response time; Sojourn time        

Problem Definition

The problem is concerned with efficiently scheduling jobs on a system with multiple resources to provide a good quality of service. In scheduling literature, several models have been considered to model the problem setting and several different measures of quality have been studied. This note considers the following model: There are several identical machines, and jobs are released over time. Each job is characterized by its size, which is the amount of processing it must receive to be completed, and its release time, before which it cannot be scheduled. In this model, Leonardi and Raz studied the objective of minimizing the average flow time of the jobs, where the flow time of a job is duration of time since it is released until its processing requirement is met. Flow time is also referred to as response time or sojourn time and is a very natural and commonly used measure of the quality of a schedule.

Notations

Let \(...

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   399.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Recommended Reading

  1. Avrahami, N., Azar, Y.: Minimizing total flow time and completion time with immediate dispacthing. In: Proceedings of 15th SPAA, pp. 11–18. (2003)

    Google Scholar 

  2. Awerbuch, B., Azar, Y., Leonardi, S., Regev, O.: Minimizing the flow time without migration. SIAM J. Comput. 31, 1370–1382 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bansal, N.: Minimizing flow time on a constant number of machines with preemption. Oper. Res. Lett. 33, 267–273 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Garg, N., Kumar, A.: Better algorithms for minimizing average flow-time on related machines. In: Proceesings of ICALP, pp. 181–190 (2006)

    Google Scholar 

  5. Garg, N., Kumar, A.: Minimizing average flow time on related machines. In: ACM Symposium on Theory of Compuring (STOC), pp. 730–738 (2006)

    Google Scholar 

  6. Kellerer, H., Tautenhahn, T., Woeginger, G.J.: Approximability and nonapproximability results for minimizing total flow time on a single machine. SIAM J. Comput. 28, 1155–1166 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Leonardi, S.: A simpler proof of preemptive flow-time approximation. Approximation and On-line Algorithms. In: Bampis, E. (ed.) Lecture Notes in Computer Science. Springer, Berlin (2003)

    Google Scholar 

  8. Leonardi, S., Raz, D.: Approximating total flow time on parallel machines. In: ACM Symposium on Theory of Computing (STOC), pp. 110–119 (1997)

    Google Scholar 

  9. Pruhs, K., Sgall, J., Torng, E.: Online scheduling. In: Handbook on Scheduling: Algorithms, Models and Performance Analysis, CRC press (2004). Symposium on Theory of Computing (STOC), pp. 110–119. (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IBM Research, IBM, Yorktown Heights, NY, USA

    Nikhil Bansal

Authors
  1. Nikhil Bansal
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

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

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Bansal, N. (2008). Minimum Flow Time. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_235

Download citation

Publish with us

Policies and ethics

Search

Navigation