Optimal Edge Weight Perturbations to Attack Shortest Paths

TL;DR

This paper introduces the Force Path Problem, a polynomial-time method for adversaries to manipulate network edge weights to make a specific path shortest, with significant reductions in perturbation needed compared to baseline methods.

Contribution

It formulates the Force Path Problem, proves its polynomial solvability, and presents the PATHPERTURB algorithm for effective edge weight perturbation in networks.

Findings

Optimal perturbation often halves the budget compared to greedy methods.

The PATHPERTURB algorithm efficiently solves the Force Path Problem.

Applicable to synthetic and real networks with varied structures.

Abstract

Finding shortest paths in a given network (e.g., a computer network or a road network) is a well-studied task with many applications. We consider this task under the presence of an adversary, who can manipulate the network by perturbing its edge weights to gain an advantage over others. Specifically, we introduce the Force Path Problem as follows. Given a network, the adversary's goal is to make a specific path the shortest by adding weights to edges in the network. The version of this problem in which the adversary can cut edges is NP-complete. However, we show that Force Path can be solved to within arbitrary numerical precision in polynomial time. We propose the PATHPERTURB algorithm, which uses constraint generation to build a set of constraints that require paths other than the adversary's target to be sufficiently long. Across a highly varied set of synthetic and real networks, we show that the optimal solution often reduces the required perturbation budget by about half when compared to a greedy baseline method.