A Chance-Constrained Programming Model for Inverse Spanning Tree Problem with Uncertain Edge Weights

The inverse spanning tree problem is to make a given spanning tree be a minimum spanning tree on a connected graph via a minimum perturbation on its edge weights. In this paper, a chance-constrained programming model is proposed to handle the inverse spanning tree problem where the edge weights are assumed to be uncertain variables. It is shown that such an uncertain minimum spanning tree can be characterized by some constraints on the paths of the graph. Consequently, the proposed model can be reformulated into a deterministic programming model. Furthermore, when the edge weights are linear uncertain variables, the corresponding model reduces to a linear programming problem and can be solved efficiently.