Maintaining source–destination connectivity in uncertain networks under adversarial attack

Abstract

This paper investigates the problem of maintaining the connectivity between two vertices, a source and a destination, in an uncertain network under adversarial attack, where a defender preserves crucial links to prevent the source–destination vertex pair from being disconnected by an attacker. In contrast with prior art that mostly focuses on the overall network connectivity, in this work connectivity maintenance is restricted to a pair of selected vertices, which may provide insights into reliable point-to-point connection. We model the network as a random graph where each link carries both an existence probability and a probing cost, and seek to design a defensive strategy that ensures source–destination connectivity under minimum probing expenditure, regardless of adversarial behavior. To this end, we first delve into the computational complexity of the problem by establishing its NP-hardness, and put forth an optimal defensive strategy leveraging dynamic programming. Due to the prohibitive price of attaining optimality, we further design two approximate defensive strategies aimed at pursuing effective defensive performance within polynomial time, in which the first one is a path-based heuristic strategy that iteratively extends a preserved path by probing links with high utility regarding source–destination connectivity, and the second one is a cut-based minimax strategy that prioritizes the links in the minimum potential source–destination cut in order to minimize the possible worst-case loss suffered by the defender with a constant approximation ratio. Extensive experiments conducted on synthetic and real-world network datasets under diverse attacking strategies validate the superiority of the proposed strategies in both effectiveness and robustness over baselines.