Skip to main content
SpringerLink
Log in

Semi-online Preemptive Scheduling: Study of Special Cases

  • Conference paper
Parallel Processing and Applied Mathematics (PPAM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6068))

Abstract

We use the duality of linear programing to obtain exact formulas of competitive ratio for the semi-online preemptive scheduling on three and four machines. We use the linear programs from [3]. Namely we consider the online scheduling and the semi-online scheduling with known sum of processing times. We solve the linear programs symbolically by examining all basic solution candidates. All solutions are obtained by a computer but all are verifiable by hand.

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

Access this chapter

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Du, D.: Optimal preemptive semi-online scheduling on two uniform processors. Inform. Process. Lett. 92(5), 219–223 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ebenlendr, T., Jawor, W., Sgall, J.: Preemptive online scheduling: Optimal algorithms for all speeds. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 327–339. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Ebenlendr, T., Sgall, J.: Semi-Online Preemptive Scheduling: Online Algorithm for All Variants. In: Proc. 26st Symp. on Theoretical Aspects of Comput. Sci. (STACS), Dagstuhl Seminar Proceedings, vol. 9001, pp. 346–360, IBFI (2009)

    Google Scholar 

  4. Epstein, L., Favrholdt, L.M.: Optimal preemptive semi-online scheduling to minimize makespan on two related machines. Oper. Res. Lett. 30, 269–275 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Horwath, E., Lam, E.C., Sethi, R.: A level algorithm for preemptive scheduling. J. ACM 24, 32–43 (1977)

    Article  Google Scholar 

  6. Jiang, Y., He, Y.: Optimal semi-online algorithms for preemptive scheduling problems with inexact partial information. Theoret. Comput. Sci. 44(7-8), 571–590 (2007)

    MATH  MathSciNet  Google Scholar 

  7. Vazirani, V.V.: Approximation algorithms. In: LP duality, ch. 12. Springer, Heidelberg (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, AS CR, Žitná 25, CZ-11567, Praha 1, Czech Republic

    Tomáš Ebenlendr

Authors
  1. Tomáš Ebenlendr
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Computational and Information Sciences,, Czestochowa University of Technology,  

    Roman Wyrzykowski

  2. Department of Electrical Engineering and Computer Science, University of Tennessee, 37996-3450, Knoxville, TN, USA

    Jack Dongarra

  3. Institute of Computer and Information Science, Czestochowa University of Technology, Dabrowskiego 73, PL-42-200, Czestochowa, Poland

    Konrad Karczewski

  4. Department of Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, Building 321, 2800, Kongens Lyngby, Denmark

    Jerzy Wasniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ebenlendr, T. (2010). Semi-online Preemptive Scheduling: Study of Special Cases. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2009. Lecture Notes in Computer Science, vol 6068. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14403-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14403-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14402-8

  • Online ISBN: 978-3-642-14403-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation