PATHATTACK: Attacking Shortest Paths in Complex Networks

TL;DR

This paper introduces the Force Path Cut problem, an NP-complete challenge in graph perturbation, and proposes the PATHATTACK algorithm that efficiently approximates solutions by focusing on a small subset of paths, demonstrating high success in diverse networks.

Contribution

The paper formulates the Force Path Cut problem, proves its NP-completeness, and develops the PATHATTACK algorithm that effectively approximates solutions using constraint generation and set cover techniques.

Findings

PATHATTACK solves over 98% of cases optimally in experiments.

The algorithm considers only 5% of paths in most cases, improving efficiency.

Demonstrates effectiveness across synthetic and real-world networks.

Abstract

Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide Web. An adversary with the capability to perturb the graph might make the shortest path between two nodes route traffic through advantageous portions of the graph (e.g., a toll road he owns). In this paper, we introduce the Force Path Cut problem, in which there is a specific route the adversary wants to promote by removing a minimum number of edges in the graph. We show that Force Path Cut is NP-complete, but also that it can be recast as an instance of the Weighted Set Cover problem, enabling the use of approximation algorithms. The size of the universe for the set cover problem is potentially factorial in the number of nodes. To overcome this hurdle, we propose the PATHATTACK algorithm, which via constraint generation considers only a small subset of paths -- at most 5% of the number of edges in 99% of our experiments. Across a diverse set of synthetic and real networks, the linear programming formulation of Weighted Set Cover yields the optimal solution in over 98% of cases. We also demonstrate a time/cost tradeoff using two approximation algorithms and greedy baseline methods. This work provides a foundation for addressing similar problems and expands the area of adversarial graph mining beyond recent work on node classification and embedding.