Journal of Combinatorial Optimization

, Volume 27, Issue 3, pp 462–486 | Cite as

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

  • Grigory Pastukhov
  • Alexander Veremyev
  • Vladimir BoginskiEmail author
  • Eduardo L. Pasiliao


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.


Network design Strong attack tolerance R-Robust 2-clubs Combinatorial optimization Heuristics 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Grigory Pastukhov
    • 1
  • Alexander Veremyev
    • 1
  • Vladimir Boginski
    • 1
    Email author
  • Eduardo L. Pasiliao
    • 1
    • 2
  1. 1.Industrial and Systems Engineering DepartmentUniversity of FloridaGainesvilleUSA
  2. 2.Air Force Research LaboratoryMunitions DirectorateEglin AFBUSA

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