How informative are Minimum Spanning Tree algorithms?

Searching for combinatorial structures in weighted graphs with stochastic edge weights raises the issue of algorithmic robustness. In this paper, we investigate noisy versions of the Minimum Spanning Tree (MST) problem and compare the generalization properties of MST algorithms. An information-theoretic analysis of these MST algorithms measures the amount of information on spanning trees that is extracted from the input graph. Early stopping of an MST algorithm yields a set of approximate spanning trees with increased stability compared to the minimum spanning tree. The framework also provides insights for algorithm design when noise in combinatorial optimization is unavoidable.