🤖 AI Summary
This work addresses adversarial hijacking attacks on shortest paths in graph-structured networks, where an attacker manipulates edge weights to divert traffic away from the true shortest path. We formulate this as a Stackelberg game—introducing both zero-sum and general-sum variants—and prove its NP-hardness. To defend against such attacks, we propose a locally optimal heuristic based on linear programming relaxation that minimizes the attacker’s success probability while preserving both path recommendation accuracy and fidelity to ground-truth distances. Extensive experiments on multiple synthetic and real-world networks demonstrate that our method achieves defense costs approaching the theoretical lower bound, significantly reduces attack success rates, and maintains high-quality routing for benign users. Our key contributions are: (i) the first Stackelberg game-theoretic modeling of shortest-path robustness under edge-weight manipulation; and (ii) a scalable, interpretable optimization framework for strategic edge-weight perturbation.
📝 Abstract
Identifying shortest paths between nodes in a network is an important task in many applications. Recent work has shown that a malicious actor can manipulate a graph to make traffic between two nodes of interest follow their target path. In this paper, we develop a defense against such attacks by modifying the edge weights that users observe. The defender must balance inhibiting the attacker against any negative effects on benign users. Specifically, the defender's goals are: (a) recommend the shortest paths to users, (b) make the lengths of the shortest paths in the published graph close to those of the same paths in the true graph, and (c) minimize the probability of an attack. We formulate the defense as a Stackelberg game in which the defender is the leader and the attacker is the follower. We also consider a zero-sum version of the game in which the defender's goal is to minimize cost while achieving the minimum possible attack probability. We show that the defense problem is NP-hard and propose heuristic solutions for both the zero-sum and non-zero-sum settings. By relaxing some constraints of the original problem, we formulate a linear program for local optimization around a feasible point. We present defense results with both synthetic and real networks and show that our methods often reach the lower bound of the defender's cost.
