Improved formulations for minimum connectivity network interdiction problems

Abstract

The minimum connectivity interdiction problem seeks to remove at most k nodes from an undirected graph, such that a connectivity measure of the remaining subgraph is minimized. Examples of connectivity measures of a graph include the number of connected pairs of nodes, the size of the largest connected component, and the inverse of the number of connected components. This paper proposes improvements to mixed integer linear programming formulations from the literature. Improvements correspond to the construction of formulations with either a smaller number of constraints, or stronger formulations with increased sparsity of constraint matrices. In addition, two of the discussed problem formulations are demonstrated to provide the same value of linear programming relaxation and hence can be called equivalent. Computational experiments demonstrate that improved formulations allow us to solve some of the considered problem instances up to an order of magnitude times faster than using the recent benchmark.