IDEAS home Printed from https://ideas.repec.org/h/spr/oprchp/978-3-030-18500-8_33.html
   My bibliography  Save this book chapter

The Knapsack Problem with Conflict Graphs and Forcing Graphs of Bounded Clique-Width

In: Operations Research Proceedings 2018

Author

Listed:
  • Frank Gurski

    (University of Düsseldorf, Institute of Computer Science, Algorithmics for Hard Problems Group)

  • Carolin Rehs

    (University of Düsseldorf, Institute of Computer Science, Algorithmics for Hard Problems Group)

Abstract

The 0-1-knapsack problem is a well-known NP-hard problem in combinatorial optimization. We consider the extensions to the knapsack problem with conflict graph (KCG) and the knapsack problem with forcing graph (KFG). Within this paper we provide pseudo-polynomial solutions for KCG and KFG with co-graphs as conflict and forcing graphs and extend these solutions to conflict and forcing graphs of bounded clique-width. Our solutions are based on dynamic programming using the tree-structure representing the conflict graph and the forcing graph. Further we conclude fully polynomial time approximation schemes (FPTAS) for KCG on conflict graphs of bounded clique-width and KFG on forcing graphs of bounded clique-width. This generalizes the known results for conflict and forcing graphs of bounded tree-width of Pferschy and Schauer.

Suggested Citation

  • Frank Gurski & Carolin Rehs, 2019. "The Knapsack Problem with Conflict Graphs and Forcing Graphs of Bounded Clique-Width," Operations Research Proceedings, in: Bernard Fortz & Martine Labbé (ed.), Operations Research Proceedings 2018, pages 259-265, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-18500-8_33
    DOI: 10.1007/978-3-030-18500-8_33
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wei, Zequn & Hao, Jin-Kao & Ren, Jintong & Glover, Fred, 2023. "Responsive strategic oscillation for solving the disjunctively constrained knapsack problem," European Journal of Operational Research, Elsevier, vol. 309(3), pages 993-1009.
    2. Luiz Viana & Manoel Campêlo & Ignasi Sau & Ana Silva, 2021. "A unifying model for locally constrained spanning tree problems," Journal of Combinatorial Optimization, Springer, vol. 42(1), pages 125-150, July.
    3. Frank Gurski & Carolin Rehs, 2019. "Solutions for the knapsack problem with conflict and forcing graphs of bounded clique-width," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 411-432, June.
    4. Frank Gurski & Carolin Rehs, 2020. "Counting and enumerating independent sets with applications to combinatorial optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 439-463, June.

    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:978-3-030-18500-8_33. 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.