IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v31y2016i2d10.1007_s10878-014-9793-2.html
   My bibliography  Save this article

An approximation algorithm for the partial vertex cover problem in hypergraphs

Author

Listed:
  • Mourad El Ouali

    (University of Kiel)

  • Helena Fohlin

    (Linköping University)

  • Anand Srivastav

    (University of Kiel)

Abstract

Let $$\mathcal {H}=(V,\mathcal {E})$$ H = ( V , E ) be a hypergraph with set of vertices $$V, n:=|V|$$ V , n : = | V | and set of (hyper-)edges $$\mathcal {E}, m:=|\mathcal {E}|$$ E , m : = | E | . Let $$l$$ l be the maximum size of an edge, $$\varDelta $$ Δ be the maximum vertex degree and $$D$$ D be the maximum edge degree. The $$k$$ k -partial vertex cover problem in hypergraphs is the problem of finding a minimum cardinality subset of vertices in which at least $$k$$ k hyperedges are incident. For the case of $$k=m$$ k = m and constant $$l$$ l it known that an approximation ratio better than $$l$$ l cannot be achieved in polynomial time under the unique games conjecture (UGC) (Khot and Ragev J Comput Syst Sci, 74(3):335–349, 2008), but an $$l$$ l -approximation ratio can be proved for arbitrary $$k$$ k (Gandhi et al. J Algorithms, 53(1):55–84, 2004). The open problem in this context has been to give an $$\alpha l$$ α l -ratio approximation with $$\alpha

Suggested Citation

  • Mourad El Ouali & Helena Fohlin & Anand Srivastav, 2016. "An approximation algorithm for the partial vertex cover problem in hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 846-864, February.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:2:d:10.1007_s10878-014-9793-2
    DOI: 10.1007/s10878-014-9793-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-014-9793-2
    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/s10878-014-9793-2?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. Gerold Jäger & Anand Srivastav, 2005. "Improved Approximation Algorithms for Maximum Graph Partitioning Problems," Journal of Combinatorial Optimization, Springer, vol. 10(2), pages 133-167, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Yingli Ran & Yishuo Shi & Zhao Zhang, 2017. "Local ratio method on partial set multi-cover," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 302-313, July.

    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.
    1. Federico Della Croce & Vangelis Th. Paschos, 2014. "Efficient algorithms for the max $$k$$ -vertex cover problem," Journal of Combinatorial Optimization, Springer, vol. 28(3), pages 674-691, October.
    2. Alain Billionnet & Sourour Elloumi & Amélie Lambert & Angelika Wiegele, 2017. "Using a Conic Bundle Method to Accelerate Both Phases of a Quadratic Convex Reformulation," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 318-331, May.
    3. Bourgeois, Nicolas & Giannakos, Aristotelis & Lucarelli, Giorgio & Milis, Ioannis & Paschos, Vangelis Th., 2017. "Exact and superpolynomial approximation algorithms for the densest k-subgraph problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 894-903.

    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:31:y:2016:i:2:d:10.1007_s10878-014-9793-2. 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.