Stability and Robustness: Reliability in the World of Uncertainty

Weak edges and weak treeDefinition. A spanning tree is a weak tree if it is a MST for somerealization s of edge costs. An edge e is a weak edge if it belongsto some weak tree.Theorem.1. A spanning tree t is a weak tree iff it is a MST when the costsof every edge on this tree corresponds to its lower bounds andthe costs of other edges correspond to their upper bounds.2. Edge e is a weak edge iff there exists a MST using edge ewhere the cost of edge e is at its lower bound and the costs ofthe remaining edges are at their upper bounds.16/04/2009 Yury Nikulin, Sensitivity analysis 19