Skip to main content
SpringerLink
Log in

Sampling Methods Applied to Dense Instances of Non-Boolean Optimization Problems

  • Conference paper
  • First Online:
Randomization and Approximation Techniques in Computer Science (RANDOM 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1518))

Abstract

We study dense instances of optimization problems with variables taking values in Z p. Specifically, we study systems of functions from Z k p to Z p where the objective is to make as many functions as possible attain the value zero. We generalize earlier sampling methods and thereby construct a randomized polynomial time approximation scheme for instances with θ(n k) functions where n is the number of variables occurring in the functions.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Sanjeev Arora, David Karger, and Marek Karpinski. Polynomial time approximation schemes for dense instances of NP-hard problems. In Proc. Twenty-seventh Ann. ACM Symp. on Theory of Comp., pages 284–293. ACM, New York, 1995.

    Chapter  Google Scholar 

  2. Kazuoki Azuma. Weighted sums of certain dependent random variables. TÔhoku Mathematical Journal, 19:357–367, 1967.

    Article  MATH  MathSciNet  Google Scholar 

  3. Wenceslas Fernandez de la Vega. MAX-CUT has a randomized approximation scheme in dense graphs. Random Structures and Algorithms, 9:93–97, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  4. Alan Frieze and Ravi Kannan. Quick approximation to matrices and applications. Manuscript, July 1997.

    Google Scholar 

  5. Oded Goldreich, Shafi Goldwasser, and Dana Ron. Property testing and its connection to learning and approximation. In Proc. of 37th Ann. IEEE Symp. on Foundations of Comput. Sci., pages 339–348. IEEE Computer Society, Los Alamitos, 1996.

    Google Scholar 

  6. Johan Håstad. Some optimal inapproximability results. In Proc. Twenty-ninth Ann. ACM Symp. on Theory of Comp., pages 1–10. ACM, New York, 1997.

    Chapter  Google Scholar 

  7. Wassily Hoeffding. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 58:13–30, 1963.

    Article  MATH  MathSciNet  Google Scholar 

  8. Rajeev Motwani and Prabhakar Raghavan. Randomized Algorithms. Cambridge University Press, Cambridge, 1995.

    MATH  Google Scholar 

  9. Christos H. Papadimitriou. Computational Complexity. AddisonWestley, Reading, 1994.

    MATH  Google Scholar 

  10. Uri Zwick. Finding almost-satisfying assignments. In Proc. Thirtieth Ann. ACM Symp. on Theory of Comp., pages 551–560. ACM, New York, 1998.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Numerical Analysis and Computing Science, Royal Institute of Technology, SE-100 44, Stockholm, Sweden

    Gunnar Andersson & Lars Engebretsen

Authors
  1. Gunnar Andersson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lars Engebretsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. International Computer Science Institute, 1947 Center Street, Suite 600, Berkeley, CA, 94704-1198, USA

    Michael Luby

  2. Computer Science Department, University of Geneva, 24, rue Général Dufour, CH-1211, Geneva 4, Switzerland

    José D. P. Rolim

  3. University of Barcelona (UPC), Jordi Girona Salgado 1-3, E-08034, Barcelona, Spain

    Maria Serna

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Andersson, G., Engebretsen, L. (1998). Sampling Methods Applied to Dense Instances of Non-Boolean Optimization Problems. In: Luby, M., Rolim, J.D.P., Serna, M. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1998. Lecture Notes in Computer Science, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49543-6_28

Download citation

  • DOI: https://doi.org/10.1007/3-540-49543-6_28

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65142-0

  • Online ISBN: 978-3-540-49543-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation