Quantifying all to one network topology robustness under budget constraints

To design robust network topologies that resist strategic attacks, one must first be able to quantify robustness. In a recent line of research, the theory of network blocking games has been used to derive robustness metrics for topologies. However, these previous works did not consider the budget constraints of the network operator. In this paper, we introduce a budget limit on the operator and study two budget constraint formulations: the maximum and the expected cost constraints. For practical applications, the greatest challenge posed by blocking games is their computational complexity. Therefore, we show that the expected cost constraint formulation leads to games that can be solved efficiently, while the maximum cost constraint leads to NP-hard problems. As an illustrative example, this paper discusses the particular case of All-to-One (e.g., sensor or access) networks.