核心概念
The recoverable robust shortest path problem with discrete recourse is Σp3-hard for the arc exclusion and arc symmetric difference neighborhoods, and the inner adversarial problem for these neighborhoods is Πp2-hard.
摘要
The paper investigates the computational complexity of the recoverable robust shortest path problem with discrete recourse. The problem involves finding a first-stage path that can be modified to some extent in the second stage by applying a limited recovery action.
Key highlights:
- The problem is shown to be Σp3-hard for the arc exclusion and arc symmetric difference neighborhoods.
- The inner adversarial problem for these neighborhoods is proven to be Πp2-hard.
- The hardness results are established through reductions from the ∀(Γ)∃CNF-SAT and ∃∀(Γ)∃3CNF-SAT problems.
- The paper strengthens the known complexity results for this problem, which was previously shown to be strongly NP-hard for the arc inclusion neighborhood.
- The hardness of the adversarial problem and the recoverable robust problem are characterized for the arc exclusion and arc symmetric difference neighborhoods.