The robust spanning tree problem with interval data

Abstract

Motivated by telecommunications applications we investigate the minimum spanning tree problem where edge costs are interval numbers. Since minimum spanning trees depend on the realization of the edge costs, we de5ne the robust spanning tree problem to hedge against the worst case contingency, and present a mixed integer programming formulation of the problem. We also de5ne some useful optimality concepts, and present characterizations for these entities leading to polynomial time recognition algorithms. These entities are then used to preprocess a given graph with interval data prior to the solution of the robust spanning tree problem. Computational results show that these preprocessing procedures are quite e9ective in reducing the time to compute a robust spanning tree.