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Critical node/edge detection problems on trees

Author

Listed:
  • Marco Di Summa

    (Università degli Studi di Padova)

  • Syed Md Omar Faruk

    (Shahjalal University of Science and Technology)

Abstract

We consider the problem of removing a limited subset of nodes and/or edges from a graph in order to minimize the so-called pairwise connectivity of the residual graph, which is defined as the total cost of the pairs of nodes still connected by a path. This is a well-studied version of a family of problems known as critical node or edge detection problems. However, while most of the literature focuses on deleting nodes or edges separately, we allow the simultaneous removal of nodes and edges. We consider both the case in which the nodes and edges removed must satisfy a joint weight limit, and the case in which two separate weight limits are given for nodes and edges. We study the complexity of several problems of this type when the given graph is a tree, providing NP-hardness results or polynomial-time algorithms for the different cases that we analyze.

Suggested Citation

  • Marco Di Summa & Syed Md Omar Faruk, 2023. "Critical node/edge detection problems on trees," 4OR, Springer, vol. 21(3), pages 439-455, September.
    • Handle: RePEc:spr:aqjoor:v:21:y:2023:i:3:d:10.1007_s10288-022-00518-0
    DOI: 10.1007/s10288-022-00518-0
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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.
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