IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v28y2014i1d10.1007_s10878-014-9730-4.html
   My bibliography  Save this article

An integer programming framework for critical elements detection in graphs

Author

Listed:
  • Alexander Veremyev

    (Air Force Research Laboratory, Munitions Directorate)

  • Oleg A. Prokopyev

    (University of Pittsburgh)

  • Eduardo L. Pasiliao

    (Air Force Research Laboratory, Munitions Directorate)

Abstract

This study presents an integer programming framework for minimizing the connectivity and cohesiveness properties of a given graph by removing nodes and edges subject to a joint budgetary constraint. The connectivity and cohesiveness metrics are assumed to be general functions of sizes of the remaining connected components and node degrees, respectively. We demonstrate that our approach encompasses, as special cases (possibly, under some mild conditions), several other models existing in the literature, including minimization of the total number of connected node pairs, minimization of the largest connected component size, and maximization of the number of connected components. We discuss computational complexity issues, derive linear mixed integer programming (MIP) formulations, and describe additional modeling enhancements aimed at improving the performance of MIP solvers. We also conduct extensive computational experiments with real-life and randomly generated network instances under various settings that reveal interesting insights and demonstrate advantages and limitations of the proposed framework.

Suggested Citation

  • Alexander Veremyev & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2014. "An integer programming framework for critical elements detection in graphs," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 233-273, July.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:1:d:10.1007_s10878-014-9730-4
    DOI: 10.1007/s10878-014-9730-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-014-9730-4
    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/s10878-014-9730-4?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. Hans L. Bodlaender & Albert Hendriks & Alexander Grigoriev & Nadejda V. Grigorieva, 2010. "The Valve Location Problem in Simple Network Topologies," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 433-442, August.
    2. Ashwin Arulselvan & Clayton W. Commander & Oleg Shylo & Panos M. Pardalos, 2011. "Cardinality-Constrained Critical Node Detection Problem," Springer Optimization and Its Applications, in: Nalân Gülpınar & Peter Harrison & Berç Rüstem (ed.), Performance Models and Risk Management in Communications Systems, pages 79-91, Springer.
    3. Maarten Oosten & Jeroen H. G. C. Rutten & Frits C. R. Spieksma, 2007. "Disconnecting graphs by removing vertices: a polyhedral approach," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(1), pages 35-60, February.
    4. Myung, Young-Soo & Kim, Hyun-joon, 2004. "A cutting plane algorithm for computing k-edge survivability of a network," European Journal of Operational Research, Elsevier, vol. 156(3), pages 579-589, August.
    5. Marco Di Summa & Andrea Grosso & Marco Locatelli, 2012. "Branch and cut algorithms for detecting critical nodes in undirected graphs," Computational Optimization and Applications, Springer, vol. 53(3), pages 649-680, December.
    6. Jose L. Walteros & Panos M. Pardalos, 2012. "Selected Topics in Critical Element Detection," Springer Optimization and Its Applications, in: Nicholas J. Daras (ed.), Applications of Mathematics and Informatics in Military Science, edition 127, chapter 0, pages 9-26, Springer.
    7. Stephen P. Borgatti, 2006. "Identifying sets of key players in a social network," Computational and Mathematical Organization Theory, Springer, vol. 12(1), pages 21-34, April.
    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. Hooshmand, F. & Mirarabrazi, F. & MirHassani, S.A., 2020. "Efficient Benders decomposition for distance-based critical node detection problem," Omega, Elsevier, vol. 93(C).
    2. Bahram Alidaee & Haibo Wang & Jun Huang & Lutfu S. Sua, 2023. "Integrating Statistical Simulation and Optimization for Redundancy Allocation in Smart Grid Infrastructure," Energies, MDPI, vol. 17(1), pages 1-13, December.
    3. Mahdavi Pajouh, Foad & Walteros, Jose L. & Boginski, Vladimir & Pasiliao, Eduardo L., 2015. "Minimum edge blocker dominating set problem," European Journal of Operational Research, Elsevier, vol. 247(1), pages 16-26.
    4. Zhou, Yangming & Wang, Gezi & Hao, Jin-Kao & Geng, Na & Jiang, Zhibin, 2023. "A fast tri-individual memetic search approach for the distance-based critical node problem," European Journal of Operational Research, Elsevier, vol. 308(2), pages 540-554.
    5. Matsypura, Dmytro & Prokopyev, Oleg A. & Zahar, Aizat, 2018. "Wildfire fuel management: Network-based models and optimization of prescribed burning," European Journal of Operational Research, Elsevier, vol. 264(2), pages 774-796.
    6. Wei, Ningji & Walteros, Jose L., 2022. "Integer programming methods for solving binary interdiction games," European Journal of Operational Research, Elsevier, vol. 302(2), pages 456-469.
    7. Bernardetta Addis & Roberto Aringhieri & Andrea Grosso & Pierre Hosteins, 2016. "Hybrid constructive heuristics for the critical node problem," Annals of Operations Research, Springer, vol. 238(1), pages 637-649, March.
    8. Foad Mahdavi Pajouh, 2020. "Minimum cost edge blocker clique problem," Annals of Operations Research, Springer, vol. 294(1), pages 345-376, November.
    9. Chen, Wei & Jiang, Manrui & Jiang, Cheng & Zhang, Jun, 2020. "Critical node detection problem for complex network in undirected weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    10. Marco Di Summa & Syed Md Omar Faruk, 2023. "Critical node/edge detection problems on trees," 4OR, Springer, vol. 21(3), pages 439-455, September.
    11. Alexander Veremyev & Konstantin Pavlikov & Eduardo L. Pasiliao & My T. Thai & Vladimir Boginski, 2019. "Critical nodes in interdependent networks with deterministic and probabilistic cascading failures," Journal of Global Optimization, Springer, vol. 74(4), pages 803-838, August.
    12. Lordan, Oriol & Albareda-Sambola, Maria, 2019. "Exact calculation of network robustness," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 276-280.
    13. Ningji Wei & Jose L. Walteros & Foad Mahdavi Pajouh, 2021. "Integer Programming Formulations for Minimum Spanning Tree Interdiction," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1461-1480, October.
    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. Ventresca, Mario & Harrison, Kyle Robert & Ombuki-Berman, Beatrice M., 2018. "The bi-objective critical node detection problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 895-908.
    16. Zhong, Haonan & Mahdavi Pajouh, Foad & A． Prokopyev, Oleg, 2023. "On designing networks resilient to clique blockers," European Journal of Operational Research, Elsevier, vol. 307(1), pages 20-32.
    17. Bernardetta Addis & Roberto Aringhieri & Andrea Grosso & Pierre Hosteins, 2016. "Hybrid constructive heuristics for the critical node problem," Annals of Operations Research, Springer, vol. 238(1), pages 637-649, March.

    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. Chen, Wei & Jiang, Manrui & Jiang, Cheng & Zhang, Jun, 2020. "Critical node detection problem for complex network in undirected weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    2. T. N. Dinh & M. T. Thai & H. T. Nguyen, 2014. "Bound and exact methods for assessing link vulnerability in complex networks," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 3-24, July.
    3. Gokhan Karakose & Ronald G. McGarvey, 2019. "Optimal Detection of Critical Nodes: Improvements to Model Structure and Performance," Networks and Spatial Economics, Springer, vol. 19(1), pages 1-26, March.
    4. Hosseinali Salemi & Austin Buchanan, 2022. "Solving the Distance-Based Critical Node Problem," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1309-1326, May.
    5. Marco Di Summa & Syed Md Omar Faruk, 2023. "Critical node/edge detection problems on trees," 4OR, Springer, vol. 21(3), pages 439-455, September.
    6. César Yajure & Darihelen Montilla & Jose Emmanuel Ramirez-Marquez & Claudio M Rocco S, 2013. "Network vulnerability assessment via bi-objective optimization with a fragmentation approach as proxy," Journal of Risk and Reliability, , vol. 227(6), pages 576-585, December.
    7. Joe Naoum-Sawaya & Christoph Buchheim, 2016. "Robust Critical Node Selection by Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 162-174, February.
    8. Bernardetta Addis & Roberto Aringhieri & Andrea Grosso & Pierre Hosteins, 2016. "Hybrid constructive heuristics for the critical node problem," Annals of Operations Research, Springer, vol. 238(1), pages 637-649, March.
    9. Ningji Wei & Jose L. Walteros & Foad Mahdavi Pajouh, 2021. "Integer Programming Formulations for Minimum Spanning Tree Interdiction," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1461-1480, October.
    10. Huff, Johnathon D. & Leonard, William B. & Medal, Hugh R., 2022. "The wireless network jamming problem subject to protocol interference using directional antennas and with battery capacity constraints," International Journal of Critical Infrastructure Protection, Elsevier, vol. 39(C).
    11. Hooshmand, F. & Mirarabrazi, F. & MirHassani, S.A., 2020. "Efficient Benders decomposition for distance-based critical node detection problem," Omega, Elsevier, vol. 93(C).
    12. Ventresca, Mario & Harrison, Kyle Robert & Ombuki-Berman, Beatrice M., 2018. "The bi-objective critical node detection problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 895-908.
    13. Bernardetta Addis & Roberto Aringhieri & Andrea Grosso & Pierre Hosteins, 2016. "Hybrid constructive heuristics for the critical node problem," Annals of Operations Research, Springer, vol. 238(1), pages 637-649, March.
    14. Alexander Veremyev & Konstantin Pavlikov & Eduardo L. Pasiliao & My T. Thai & Vladimir Boginski, 2019. "Critical nodes in interdependent networks with deterministic and probabilistic cascading failures," Journal of Global Optimization, Springer, vol. 74(4), pages 803-838, August.
    15. Faramondi, Luca & Setola, Roberto & Panzieri, Stefano & Pascucci, Federica & Oliva, Gabriele, 2018. "Finding critical nodes in infrastructure networks," International Journal of Critical Infrastructure Protection, Elsevier, vol. 20(C), pages 3-15.
    16. Alexander Veremyev & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2019. "Finding Critical Links for Closeness Centrality," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 367-389, April.
    17. Mark J. O. Bagley, 2019. "Networks, geography and the survival of the firm," Journal of Evolutionary Economics, Springer, vol. 29(4), pages 1173-1209, September.
    18. Foad Mahdavi Pajouh, 2020. "Minimum cost edge blocker clique problem," Annals of Operations Research, Springer, vol. 294(1), pages 345-376, November.
    19. Raddant, Matthias & Takahashi, Hiroshi, 2019. "The Japanese corporate board network," Kiel Working Papers 2130, Kiel Institute for the World Economy (IfW Kiel).
    20. Karakose, Gokhan & McGarvey, Ronald G., 2018. "Capacitated path-aggregation constraint model for arc disruption in networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 225-238.

    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:28:y:2014:i:1:d:10.1007_s10878-014-9730-4. 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.