Connectivity Maintenance in Uncertain Networks under Adversarial Attack

Abstract

This paper studies the problem of connectivity maintenance in adversarial uncertain networks, where a defender prevents the largest connected component from being decomposed by an attacker. In contrast with its deterministic counterpart, connectivity maintenance in an uncertain network involves additional testing on edges to determine their existence. To this end, by modeling a general uncertain network as a random graph with each edge associated with an existence probability and a testing cost, our goal is to design a general adaptive defensive strategy to maximize the expected size of the largest remaining connected component with minimum expected testing cost and, moreover, the strategy should be independent of the attacking patterns. The computational complexity of the connectivity maintenance problem is unraveled by proving its NP-hardness. To accurately tackle the problem, based on dynamic programming we first propose an optimal defensive strategy for a specific class of uncertain networks with uniform testing costs. Thereafter multi-objective optimization is adopted to generalize the optimal strategy for general uncertain networks through weighted sum of normalized size and cost. Due to the prohibitive price of an optimal strategy, two approximate defensive strategies are further designed to pursue decent performance with quasilinear complexity. We first derive a heuristic approach by quantifying the edge vulnerability through an analogy from the degree centrality in deterministic networks to the probability degree and connectivity weight in uncertain networks. For performance guarantee, we then devise 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 caused by the attacker and has an approximation ratio of (1 − 1/e). Extensive experiments on both synthetic and real-world network datasets under diverse attacking patterns demonstrate the superiority of the proposed strategies over baselines.