IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v29y2015i4d10.1007_s10878-013-9629-5.html
   My bibliography  Save this article

Parameterizations of hitting set of bundles and inverse scope

Author

Listed:
  • Peter Damaschke

    (Chalmers University)

Abstract

Hitting Set of Bundles generalizes the ordinary Hitting Set problem in the way that prescribed bundles of elements rather than single elements have to be put in a hitting set. The goal is to minimize the total number of distinct elements in the solution. First we prove that Hitting Set of Bundles, with the number of hyperedges and the solution size as parameter, is $$W[1]$$ W [ 1 ] -complete. This contrasts to the to the corresponding parameterized Hitting Set version which is in FPT. Then we use this result to prove $$W[i]$$ W [ i ] -hardness also for the Inverse Scope problem and some of its variants. This problem asks to identify small sets of chemical reactants being able to produce a given set of target compounds in a network of reactions. The problem has a graph-theoretic formulation as a reachability problem in directed graphs. On the positive side, we give an FPT algorithm where the parameter is the total number of compounds involved in the reactions.

Suggested Citation

  • Peter Damaschke, 2015. "Parameterizations of hitting set of bundles and inverse scope," Journal of Combinatorial Optimization, Springer, vol. 29(4), pages 847-858, May.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:4:d:10.1007_s10878-013-9629-5
    DOI: 10.1007/s10878-013-9629-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-013-9629-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-013-9629-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter Damaschke, 2009. "Multiple hypernode hitting sets and smallest two-cores with targets," Journal of Combinatorial Optimization, Springer, vol. 18(3), pages 294-306, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:jcomop:v:29:y:2015:i:4:d:10.1007_s10878-013-9629-5. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.