IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v21y2013i1p13-25.html
   My bibliography  Save this article

New heuristics for the vertex coloring problem based on semidefinite programming

Author

Listed:
  • Jelena Govorčin
  • Nebojša Gvozdenović
  • Janez Povh

Abstract

The Lovász theta number Lovász (IEEE Trans Inf Theory 25:1–7, 1979 ) is a well-known lower bound on the chromatic number of a graph $$G$$ , and $$\varPsi _K(G)$$ is its impressive strengthening Gvozdenović and Laurent (SIAM J Optim 19(2):592–615, 2008 ). The bound $$\varPsi _K(G)$$ was introduced in very specific and abstract setting which is tough to translate into usual mathematical programming framework. In the first part of this paper we unify the motivations and approaches to both bounds and rewrite them in a very similar settings which are easy to understand and straightforward to implement. In the second part of the paper we provide explanations how to solve efficiently the resulting semidefinite programs and how to use optimal solutions to get good coloring heuristics. We propose two vertex coloring heuristics based on $$\varPsi _K(G)$$ and present numerical results on medium sized graphs. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Jelena Govorčin & Nebojša Gvozdenović & Janez Povh, 2013. "New heuristics for the vertex coloring problem based on semidefinite programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 13-25, June.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:1:p:13-25
    DOI: 10.1007/s10100-012-0276-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10100-012-0276-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10100-012-0276-1?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. Gvozdenovic, N. & Laurent, M. & Vallentin, F., 2009. "Block-diagonal semidenfinite programming hierarchies for 0/1 programming," Other publications TiSEM 32708817-eaaf-4337-9962-b, Tilburg University, School of Economics and Management.
    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. Tibor Csendes & Lidija Zadnik Stirn & Janez Žerovnik, 2013. "Editorial," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 1-2, June.
    2. Zehui Shao & Aleksander Vesel, 2015. "$$L(3,2,1)$$ L ( 3 , 2 , 1 ) -labeling of triangular and toroidal grids," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(3), pages 659-673, September.
    3. Andrej Kastrin & Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2021. "Methodologies and applications for resilient global development from the aspect of SDI-SOR special issues of CJOR," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 773-790, September.

    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:cejnor:v:21:y:2013:i:1:p:13-25. 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.