The Interdiction Problem for the Minimum Spanning Tree
Abstract
In this presentation, we consider the Minimum Spanning Tree Interdiction (MSTI) problem. This problem is a two-player game between a network operator and an interdictor. The former aims to determine a Minimum Spanning Tree (MST) in a network. Constrained by a budget, the latter seeks to change the network topology to increase the weight of a MST. Two types of interdiction are considered: total and partial interdiction. A total interdicted edge is considered absent, while the weight of a partial interdicted edge is augmented by a predefined amount. The interdictor's budget is modeled as a cardinality, each edge has the same interdiction cost, or as a knapsack constraint, the interdiction costs might be different. Four mathematical formulations for a generalization of the MSTI problem are devised. In addition, valid inequalities are proposed to strengthen one of the models. Furthermore, an analysis of the dominance relations between the models is carried out. Finally, computational experiments are presented to evaluate the efficiency of our formulations.