Minimum spanning trees in networks with varying edge weights

This paper considers the problem of determining minimum spanning trees in networks in which each edge weight can assume a finite number of distinct values. We use the algebraic structure of an underlying Hasse diagram to describe the relationship between different edge-weight realizations of the network, yielding new results on how MSTs change under multiple edge-weight perturbations. We investigate various implementation strategies for updating MSTs in this manner. Computational results are provided for some challenging test networks.