IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v14y2007i4d10.1007_s10878-007-9069-1.html
   My bibliography  Save this article

The densest k-subgraph problem on clique graphs

Author

Listed:
  • Maria Liazi

    (University of Athens)

  • Ioannis Milis

    (Athens University Economics and Business)

  • Fanny Pascual

    (University of Évry)

  • Vassilis Zissimopoulos

    (University of Athens)

Abstract

The Densest k-Subgraph (DkS) problem asks for a k-vertex subgraph of a given graph with the maximum number of edges. The problem is strongly NP-hard, as a generalization of the well known Clique problem and we also know that it does not admit a Polynomial Time Approximation Scheme (PTAS). In this paper we focus on special cases of the problem, with respect to the class of the input graph. Especially, towards the elucidation of the open questions concerning the complexity of the problem for interval graphs as well as its approximability for chordal graphs, we consider graphs having special clique graphs. We present a PTAS for stars of cliques and a dynamic programming algorithm for trees of cliques.

Suggested Citation

  • Maria Liazi & Ioannis Milis & Fanny Pascual & Vassilis Zissimopoulos, 2007. "The densest k-subgraph problem on clique graphs," Journal of Combinatorial Optimization, Springer, vol. 14(4), pages 465-474, November.
    • Handle: RePEc:spr:jcomop:v:14:y:2007:i:4:d:10.1007_s10878-007-9069-1
    DOI: 10.1007/s10878-007-9069-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-007-9069-1
    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/s10878-007-9069-1?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. S. S. Ravi & D. J. Rosenkrantz & G. K. Tayi, 1994. "Heuristic and Special Case Algorithms for Dispersion Problems," Operations Research, INFORMS, vol. 42(2), pages 299-310, April.
    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.
    1. Sergey Kovalev & Isabelle Chalamon & Fabio J. Petani, 2023. "Maximizing single attribute diversity in group selection," Annals of Operations Research, Springer, vol. 320(1), pages 535-540, January.
    2. Felix Prause & Kai Hoppmann-Baum & Boris Defourny & Thorsten Koch, 2021. "The maximum diversity assortment selection problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 521-554, June.
    3. Hunting, Marcel & Faigle, Ulrich & Kern, Walter, 2001. "A Lagrangian relaxation approach to the edge-weighted clique problem," European Journal of Operational Research, Elsevier, vol. 131(1), pages 119-131, May.
    4. Parreño, Francisco & Álvarez-Valdés, Ramón & Martí, Rafael, 2021. "Measuring diversity. A review and an empirical analysis," European Journal of Operational Research, Elsevier, vol. 289(2), pages 515-532.
    5. Rennen, G., 2008. "Subset Selection from Large Datasets for Kriging Modeling," Discussion Paper 2008-26, Tilburg University, Center for Economic Research.
    6. Tetsuya Araki & Shin-ichi Nakano, 0. "Max–min dispersion on a line," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-7.
    7. Erkut, E. & ReVelle, C. & Ulkusal, Y., 1996. "Integer-friendly formulations for the r-separation problem," European Journal of Operational Research, Elsevier, vol. 92(2), pages 342-351, July.
    8. Spiers, Sandy & Bui, Hoa T. & Loxton, Ryan, 2023. "An exact cutting plane method for the Euclidean max-sum diversity problem," European Journal of Operational Research, Elsevier, vol. 311(2), pages 444-454.
    9. Prokopyev, Oleg A. & Kong, Nan & Martinez-Torres, Dayna L., 2009. "The equitable dispersion problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 59-67, August.
    10. Anna Martínez-Gavara & Vicente Campos & Manuel Laguna & Rafael Martí, 2017. "Heuristic solution approaches for the maximum minsum dispersion problem," Journal of Global Optimization, Springer, vol. 67(3), pages 671-686, March.
    11. Nicolas Dupin & Frank Nielsen & El-Ghazali Talbi, 2021. "Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front," Mathematics, MDPI, vol. 9(4), pages 1-30, February.
    12. Wu, Qinghua & Hao, Jin-Kao, 2015. "A review on algorithms for maximum clique problems," European Journal of Operational Research, Elsevier, vol. 242(3), pages 693-709.
    13. Balabhaskar Balasundaram & Sergiy Butenko & Illya V. Hicks, 2011. "Clique Relaxations in Social Network Analysis: The Maximum k -Plex Problem," Operations Research, INFORMS, vol. 59(1), pages 133-142, February.
    14. Lei, Ting L. & Church, Richard L., 2015. "On the unified dispersion problem: Efficient formulations and exact algorithms," European Journal of Operational Research, Elsevier, vol. 241(3), pages 622-630.
    15. Rennen, G., 2008. "Subset Selection from Large Datasets for Kriging Modeling," Other publications TiSEM 9dfe6396-1933-45c0-b4e3-5, Tilburg University, School of Economics and Management.
    16. Zhicheng Liu & Longkun Guo & Donglei Du & Dachuan Xu & Xiaoyan Zhang, 2022. "Maximization problems of balancing submodular relevance and supermodular diversity," Journal of Global Optimization, Springer, vol. 82(1), pages 179-194, January.
    17. Erdoğan, Güneş & Battarra, Maria & Rodríguez-Chía, Antonio M., 2022. "The hub location and pricing problem," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1035-1047.
    18. Şenay Ağca & Burak Eksioglu & Jay B. Ghosh, 2000. "Lagrangian solution of maximum dispersion problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(2), pages 97-114, March.
    19. Sayyady, Fatemeh & Fathi, Yahya, 2016. "An integer programming approach for solving the p-dispersion problem," European Journal of Operational Research, Elsevier, vol. 253(1), pages 216-225.
    20. Daniel J. Rosenkrantz & Giri K. Tayi & S.S. Ravi, 2000. "Facility Dispersion Problems Under Capacity and Cost Constraints," Journal of Combinatorial Optimization, Springer, vol. 4(1), pages 7-33, March.

    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:14:y:2007:i:4:d:10.1007_s10878-007-9069-1. 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.