On designing networks resilient to clique blockers

Robustness and vulnerability analysis of networked systems is often performed using the concept of vertex blockers. In particular, in the minimum cost vertex blocker clique problem, we seek a subset of vertices with the minimum total blocking cost such that the weight of any remaining clique in the interdicted graph (after the vertices are blocked) is upper bounded by some pre-defined parameter. Loosely speaking, we aim at disrupting the network with the minimum possible cost in order to guarantee that the network does not contain cohesive (e.g., closely related) groups of its structural elements with large weights; such groups are modeled as weighted cliques. In this paper, our focus is on designing networks that are resilient to clique blockers. Specifically, we construct additional connections (edges) in the network and our goal is to ensure (at the minimum possible cost of newly added edges) that the adversarial decision-maker (or the worst-case realization of random failures) cannot disrupt the network (namely, the weight of its cohesive groups) at some sufficiently low cost. The proposed approach is useful for modeling effective formation and preservation of influential clusters in networked systems. We first explore structural properties of our problem. Then, we develop several exact solution schemes based on integer programming and combinatorial branch-and-bound techniques. Finally, the performance of our approaches is explored in a computational study with randomly-generated and real-life network instances.