Skip to main content
SpringerLink
Log in

An Analysis of Quantified Linear Programs

  • Conference paper
  • First Online:
Discrete Mathematics and Theoretical Computer Science (DMTCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2731))

Abstract

Quantified Linear Programming is the problem of checking whether a polyhedron specified by a linear system of inequalities is nonempty, with respect to a specified quantifier string. Quantified Linear Programming subsumes traditional Linear Programming, since in traditional Linear Programming, all the program variables are existentially quantified (implicitly), whereas, in Quantified Linear Programming, a program variable may be existentially quantified or universally quantified over a continuous range. On account of the alternation of quantifiers in the specification of a Quantified Linear Program (QLP), this problem is non-trivial.

This research has been supported in part by the Air Force Office of Scientific Research under Grant F49620-02-1-0043.

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. R.P. Anstee and M. Farber. Characterizations of totally balanced matrices. J. Algorithms, 5:215–230, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  2. R.P. Anstee. Properties of (0,1)-matrices with no triangles. J. of Combinatorial Theory (A), 29:186–198, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  3. G. B. Dantzig and B. C. Eaves. Fourier-Motzkin Elimination and its Dual. Journal of Combinatorial Theory (A), 14:288–297, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  4. R. Gerber, W. Pugh, and M. Saksena. Parametric Dispatching of Hard Real-Time Tasks. IEEE Transactions on Computers, 1995.

    Google Scholar 

  5. Neil Immerman. Personal Communication.

    Google Scholar 

  6. D.S. Johnson. Personal Communication.

    Google Scholar 

  7. G. L. Nemhauser and L. A. Wolsey. Integer and Combinatorial Optimization. John Wiley & Sons, New York, 1999.

    MATH  Google Scholar 

  8. Christos H. Papadimitriou. Computational Complexity. Addison-Wesley, New York, 1994.

    MATH  Google Scholar 

  9. Alexander Schrijver. Theory of Linear and Integer Programming. John Wiley and Sons, New York, 1987.

    Google Scholar 

  10. K. Subramani. Duality in the Parametric Polytope and its Applications to a Scheduling Problem. PhD thesis, University of Maryland, College Park, August 2000.

    Google Scholar 

  11. K. Subramani. A specification framework for real-time scheduling. In W.I. Grosky and F. Plasil, editors, Proceedings of the 29th Annual Conference on Current Trends in Theory and Practice of Informatics (SOFSEM), volume 2540 of Lecture Notes in Computer Science, pages 195–207. Springer-Verlag, Nov. 2002.

    Google Scholar 

  12. V. Chandru and M.R. Rao. Linear programming. In Algorithms and Theory of Computation Handbook, CRC Press, 1999. CRC Press, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LCSEE, West Virginia University, Morgantown, WV, USA

    K. Subramani

Authors
  1. K. Subramani
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Auckland, Maths-Physics Building 303, 38 Princes St., Auckland, New Zealand

    Cristian S. Calude  & Michael J. Dinneen  & 

  2. Université de Bourgogne, LE2I, B.P. 47870, 21078, Dijon Cedex, France

    Vincent Vajnovszki

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Subramani, K. (2003). An Analysis of Quantified Linear Programs. In: Calude, C.S., Dinneen, M.J., Vajnovszki, V. (eds) Discrete Mathematics and Theoretical Computer Science. DMTCS 2003. Lecture Notes in Computer Science, vol 2731. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45066-1_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-45066-1_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40505-4

  • Online ISBN: 978-3-540-45066-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation