IDEAS home Printed from https://ideas.repec.org/h/spr/oprchp/978-3-030-48439-2_39.html
   My bibliography  Save this book chapter

Algorithms and Complexity for the Almost Equal Maximum Flow Problem

In: Operations Research Proceedings 2019

Author

Listed:
  • R. Haese

    (University of Kaiserslautern)

  • T. Heller

    (Fraunhofer ITWM)

  • S. O. Krumke

    (University of Kaiserslautern)

Abstract

In the Equal Maximum Flow Problem (EMFP), we aim for a maximum flow where we require the same flow value on all arcs in some given subsets of the arc set. We study the related Almost Equal Maximum Flow Problems (AEMFP) where the flow values on arcs of one homologous arc set differ at most by the valuation of a so called homologous function Δ. We prove that the integer AEMFP is in general N P $$\mathcal {N}\mathcal {P}$$ -complete, and that even finding a fractional maximum flow in the case of convex homologous functions is also N P $$\mathcal {N}\mathcal {P}$$ -complete. This is in contrast to the EMFP, which is polynomial time solvable in the fractional case. We also provide inapproximability results for the integral AEMFP. For the integer AEMFP we state a polynomial algorithm for the constant deviation and concave case for a fixed number of homologous sets.

Suggested Citation

  • R. Haese & T. Heller & S. O. Krumke, 2020. "Algorithms and Complexity for the Almost Equal Maximum Flow Problem," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 323-329, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-48439-2_39
    DOI: 10.1007/978-3-030-48439-2_39
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:oprchp:978-3-030-48439-2_39. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.