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

Authors:
Grigory Pastukhov;Alexander Veremyev;Vladimir Boginski;Eduardo L. Pasiliao
Affiliations:
Industrial and Systems Engineering Department, University of Florida, Gainesville, USA 32611;Industrial and Systems Engineering Department, University of Florida, Gainesville, USA 32611;Industrial and Systems Engineering Department, University of Florida, Gainesville, USA 32611;Industrial and Systems Engineering Department, University of Florida, Gainesville, USA 32611 and Air Force Research Laboratory, Munitions Directorate, Eglin AFB, USA 32542
Venue:
Journal of Combinatorial Optimization
Year:
2014

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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.