IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v27y2014i3d10.1007_s10878-012-9523-6.html
   My bibliography  Save this article

Optimal design and augmentation of strongly attack-tolerant two-hop clusters in directed networks

Author

Listed:
  • Grigory Pastukhov

    (University of Florida)

  • Alexander Veremyev

    (University of Florida)

  • Vladimir Boginski

    (University of Florida)

  • Eduardo L. Pasiliao

    (University of Florida
    Munitions Directorate)

Abstract

We consider the problems of minimum-cost design and augmentation of directed network clusters that have diameter 2 and maintain the same diameter after the deletion of up to R elements (nodes or arcs) anywhere in the cluster. The property of a network to maintain not only the overall connectivity, but also the same diameter after the deletion of multiple nodes/arcs is referred to as strong attack tolerance. This paper presents the proof of NP-completeness of the decision version of the problem, derives tight theoretical bounds, as well as develops a heuristic algorithm for the considered problems, which are extremely challenging to solve to optimality even for small networks. Computational experiments suggest that the proposed heuristic algorithm does identify high-quality near-optimal solutions; moreover, in the special case of undirected networks with identical arc construction costs, the algorithm provably produces an exact optimal solution to strongly attack-tolerant two-hop network design problem, regardless of the network size.

Suggested Citation

  • Grigory Pastukhov & Alexander Veremyev & Vladimir Boginski & Eduardo L. Pasiliao, 2014. "Optimal design and augmentation of strongly attack-tolerant two-hop clusters in directed networks," Journal of Combinatorial Optimization, Springer, vol. 27(3), pages 462-486, April.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:3:d:10.1007_s10878-012-9523-6
    DOI: 10.1007/s10878-012-9523-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-012-9523-6
    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/s10878-012-9523-6?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. Balabhaskar Balasundaram & Sergiy Butenko & Svyatoslav Trukhanov, 2005. "Novel Approaches for Analyzing Biological Networks," Journal of Combinatorial Optimization, Springer, vol. 10(1), pages 23-39, August.
    2. Robert Mokken, 1979. "Cliques, clubs and clans," Quality & Quantity: International Journal of Methodology, Springer, vol. 13(2), pages 161-173, April.
    3. Pirkul, Hasan & Soni, Samit, 2003. "New formulations and solution procedures for the hop constrained network design problem," European Journal of Operational Research, Elsevier, vol. 148(1), pages 126-140, July.
    4. BOTTON, Quentin & FORTZ, Bernard & GOUVEIA, Luis & POSS, Michael, 2011. "Benders decomposition for the hop-constrained survivable network design problem," LIDAM Discussion Papers CORE 2011037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Juan Ma & Foad Mahdavi Pajouh & Balabhaskar Balasundaram & Vladimir Boginski, 2016. "The Minimum Spanning k -Core Problem with Bounded CVaR Under Probabilistic Edge Failures," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 295-307, May.
    2. Juan Ma & Balabhaskar Balasundaram, 2019. "On the chance-constrained minimum spanning k-core problem," Journal of Global Optimization, Springer, vol. 74(4), pages 783-801, August.

    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. Alexander Veremyev & Vladimir Boginski & Eduardo Pasiliao, 2015. "Analytical characterizations of some classes of optimal strongly attack-tolerant networks and their Laplacian spectra," Journal of Global Optimization, Springer, vol. 61(1), pages 109-138, January.
    2. Veremyev, Alexander & Boginski, Vladimir & Pasiliao, Eduardo L. & Prokopyev, Oleg A., 2022. "On integer programming models for the maximum 2-club problem and its robust generalizations in sparse graphs," European Journal of Operational Research, Elsevier, vol. 297(1), pages 86-101.
    3. Komusiewicz, Christian & Nichterlein, André & Niedermeier, Rolf & Picker, Marten, 2019. "Exact algorithms for finding well-connected 2-clubs in sparse real-world graphs: Theory and experiments," European Journal of Operational Research, Elsevier, vol. 275(3), pages 846-864.
    4. Filipa D. Carvalho & Maria Teresa Almeida, 2017. "The triangle k-club problem," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 814-846, April.
    5. Maciej Rysz & Foad Mahdavi Pajouh & Pavlo Krokhmal & Eduardo L. Pasiliao, 2018. "Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights," Annals of Operations Research, Springer, vol. 262(1), pages 89-108, March.
    6. Buchanan, Austin & Sung, Je Sang & Boginski, Vladimir & Butenko, Sergiy, 2014. "On connected dominating sets of restricted diameter," European Journal of Operational Research, Elsevier, vol. 236(2), pages 410-418.
    7. Zhuqi Miao & Balabhaskar Balasundaram, 2020. "An Ellipsoidal Bounding Scheme for the Quasi-Clique Number of a Graph," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 763-778, July.
    8. Almeida, Maria Teresa & Carvalho, Filipa D., 2014. "An analytical comparison of the LP relaxations of integer models for the k-club problem," European Journal of Operational Research, Elsevier, vol. 232(3), pages 489-498.
    9. Carvalho, Filipa D. & Almeida, M. Teresa, 2011. "Upper bounds and heuristics for the 2-club problem," European Journal of Operational Research, Elsevier, vol. 210(3), pages 489-494, May.
    10. Oleksandra Yezerska & Foad Mahdavi Pajouh & Alexander Veremyev & Sergiy Butenko, 2019. "Exact algorithms for the minimum s-club partitioning problem," Annals of Operations Research, Springer, vol. 276(1), pages 267-291, May.
    11. Veremyev, Alexander & Boginski, Vladimir, 2012. "Identifying large robust network clusters via new compact formulations of maximum k-club problems," European Journal of Operational Research, Elsevier, vol. 218(2), pages 316-326.
    12. Foad Mahdavi Pajouh & Balabhaskar Balasundaram & Illya V. Hicks, 2016. "On the 2-Club Polytope of Graphs," Operations Research, INFORMS, vol. 64(6), pages 1466-1481, December.
    13. Yezerska, Oleksandra & Mahdavi Pajouh, Foad & Butenko, Sergiy, 2017. "On biconnected and fragile subgraphs of low diameter," European Journal of Operational Research, Elsevier, vol. 263(2), pages 390-400.
    14. Balasundaram, Balabhaskar & Borrero, Juan S. & Pan, Hao, 2022. "Graph signatures: Identification and optimization," European Journal of Operational Research, Elsevier, vol. 296(3), pages 764-775.
    15. Yajun Lu & Hosseinali Salemi & Balabhaskar Balasundaram & Austin Buchanan, 2022. "On Fault-Tolerant Low-Diameter Clusters in Graphs," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3181-3199, November.
    16. Foad Mahdavi Pajouh & Esmaeel Moradi & Balabhaskar Balasundaram, 2017. "Detecting large risk-averse 2-clubs in graphs with random edge failures," Annals of Operations Research, Springer, vol. 249(1), pages 55-73, February.
    17. Shahram Shahinpour & Sergiy Butenko, 2013. "Algorithms for the maximum k-club problem in graphs," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 520-554, October.
    18. Svyatoslav Trukhanov & Chitra Balasubramaniam & Balabhaskar Balasundaram & Sergiy Butenko, 2013. "Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations," Computational Optimization and Applications, Springer, vol. 56(1), pages 113-130, September.
    19. Riccardo Dondi & Mohammad Mehdi Hosseinzadeh & Giancarlo Mauri & Italo Zoppis, 2021. "Top-k overlapping densest subgraphs: approximation algorithms and computational complexity," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 80-104, January.
    20. Seiler, A. & Papanagnou, C. & Scarf, P., 2020. "On the relationship between financial performance and position of businesses in supply chain networks," International Journal of Production Economics, Elsevier, vol. 227(C).

    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:27:y:2014:i:3:d:10.1007_s10878-012-9523-6. 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.