On calculation of the stability radius for a minimum spanning tree

Abstract

We consider a minimum spanning tree problem in the situation where weights of edges are exposed to independent perturbations. We study a quantitative characteristic of stability for a given optimal solutions of the problem. The characteristic is called the stability radius and defined as the limit level of edges weights perturbations which preserve optimality of a particular solution. We present an exact formula for the stability radius that allows calculating the radius in time which is extremely close to linear with respect to number of graph edges. This improves upon a well-known formula of an optimal solution for a linear combinatorial problem which requires complete enumeration of feasible solutions set whose cardinality may grow exponentially.

Keywords

• minimum spanning tree problem
• second-best spanning tree
• sensitivity analysis of solutions
• stability radius