Computational Complexity of the Recoverable Robust Shortest Path Problem with Discrete Recourse

In this paper the recoverable robust shortest path problem is investigated. Discrete budgeted interval uncertainty representation is used to model uncertain second-stage arc costs. The known complexity results for this problem are strengthened. It is shown that it is Sigma₃ᵖ-hard for the arc exclusion and the arc symmetric difference neighborhoods. Furthermore, it is also proven that the inner adversarial problem for these neighborhoods is Pi₂ᵖ-hard.