Skip to main content
SpringerLink
Log in

The Relative Complexity of Approximate Counting Problems

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

Two natural classes of counting problems that are interreducible under approximation-preserving reductions are: (i) those that admit a particular kind of efficient approximation algorithm known as an “FPRAS”, and (ii) those that are complete for #P with respect to approximation-preserving reducibility. We describe and investigate not only these two classes but also a third class, of intermediate complexity, that is not known to be identical to (i) or (ii). The third class can be characterised as the hardest problems in a logically defined subclass of #P.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. School of Computing, University of Leeds, Leeds LS2 9JT, England

    Martin Dyer

  2. Department of Computer Science, University of Warwick, Coventry, CV4 7AL, England

    Leslie Ann Goldberg

  3. Department of Mathematics and Statistics, University of Melbourne, Parkville, Australia 3010

    Catherine Greenhill

  4. Division of Informatics, University of Edinburgh, JCMB, The King’s Buildings, Edinburgh EH9 3JZ, Scotland

    Mark Jerrum

Authors
  1. Martin Dyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leslie Ann Goldberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Catherine Greenhill
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mark Jerrum
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Martin Dyer, Leslie Ann Goldberg, Catherine Greenhill or Mark Jerrum.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dyer, M., Goldberg, L., Greenhill, C. et al. The Relative Complexity of Approximate Counting Problems. Algorithmica 38, 471–500 (2004). https://doi.org/10.1007/s00453-003-1073-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-003-1073-y

Search

Navigation