Which Link Matters? Maintaining Connectivity of Uncertain Networks Under Adversarial Attack

This article studies connectivity maintenance in uncertain networks under adversarial attack, where a defender conceals crucial links to prevent the largest connected component from being decomposed by an attacker. In contrast with its static counterpart, connectivity maintenance in uncertain networks involves additional probing on links to determine their existence. Therefore, by modeling an uncertain network as a random graph with each link associated with an existence probability and a probing cost, our goal is to design a defensive strategy for link selection that maximizes the expected size of the largest remaining connected component with the minimum expected probing cost, and moreover, the strategy should be independent of the attacking patterns. To this end, we first unravel the computational complexity of the problem by proving its NP-hardness, and then propose optimal defensive strategies based on dynamic programming and multi-objective optimization. Due to the prohibitive computational cost of optimality, two approximate defensive strategies are further designed to pursue decent performance with quasilinear complexity, in which the first one is a heuristic approach that quantifies the link vulnerability through an analogy from the degree centrality of a vertex in static networks to the connectivity weight of a link in uncertain networks, and the second one is an adaptive greedy policy incorporating the minimax rule from game theory, which minimizes the possible loss suffered by the defender in a worst-case scenario and has a constant approximation ratio. Extensive experiments on both synthetic and real-world network datasets under diverse attacking patterns demonstrate the superiority of the proposed strategies over baselines.