Skip to main content
SpringerLink
Log in

On the Hardness of Approximate Multivariate Integration

  • Conference paper
Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques (RANDOM 2003, APPROX 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2764))

Abstract

We show that it is NP-hard to \(2^{n^k}\)-approximate the integral of a positive, smooth, polynomial-time computable n-variate function, for any fixed integer k.

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. Alon, N., Yuster, R.: Uri Zwick: Color Coding. Journal of the ACM 42(4), 844–856 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Applegate, D., Kannan, R.: Sampling and Integration of Near Log-concave Functions. In: Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, pp. 156–163 (1991)

    Google Scholar 

  3. Brightwell, G., Winkler, P.: Counting Linear Extensions is #P-complete. In: Proceedings of the 23th Annual ACM Symposium on Theory of Computing, pp. 175–181 (1991)

    Google Scholar 

  4. Dyer, M., Frieze, A., Jerrum, M.: On Counting Independent Sets in Graphs. In: Proceedings of the 40nd Annual Symposium on the Foundations of Computer Science, pp. 210–217 (1999)

    Google Scholar 

  5. Dyer, M., Frieze, A., Kannan, R.: A Random Polynomial-time Algorithm for Approximating the Volume of Convex Bodies. Journal of the ACM 38, 1–17 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dyer, M., Goldberg, L.A., Greenhill, C., Jerrum, M.: On the Relative Complexity of Approximate Counting Problems. Algorithmica (to appear)

    Google Scholar 

  7. Dyer, M., Greenhill, C.: Random Walks on Combinatorial Objects. Surveys in Combinatorics 267, 101–136 (1999)

    MathSciNet  Google Scholar 

  8. Impagliazzo, R., Paturi, R.: Which Problems Have Strongly Exponential Complexity? In: Proceedings of the 39th Annual Symposiym on the Foundations of Computer Science (1998)

    Google Scholar 

  9. Papadimitriou, C.: Computational Complexity. Addison-Wesley, Reading (1994)

    MATH  Google Scholar 

  10. Sinclair, A.: Algorithms for Random Generation and Counting: A Markov Chain Approach. Progress in Theoretical Computer Science (1993)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Ioannis Koutis

Authors
  1. Ioannis Koutis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Science Department, Princeton University, 35 Olden Street, 08540, Princeton, NJ

    Sanjeev Arora

  2. Institute for Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  3. Battelle Bâtiment A, Centre Universitaire d’Informatique, Route de Drize 7, 1227, Carouge, Geneva, Switzerland

    José D. P. Rolim

  4. University of California, Los Angeles

    Amit Sahai

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Koutis, I. (2003). On the Hardness of Approximate Multivariate Integration. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds) Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques. RANDOM APPROX 2003 2003. Lecture Notes in Computer Science, vol 2764. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45198-3_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45198-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40770-6

  • Online ISBN: 978-3-540-45198-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation