Uncertain Distribution-Minimum Spanning Tree Problem

This paper investigates the minimum spanning tree problem in the framework of uncertainty theory, where the edge weights are assumed as uncertain variables. The concept of ideal uncertain minimum spanning tree is initiated by extending the definition of the uncertain α-minimum spanning tree. On the basis of this new concept, we propose the definition of uncertain distribution-minimum spanning tree in two ways. Furthermore, by using a confidence level α from the respect of cVaR in risk management, the definition of uncertain α-distributionminimum spanning tree is suggested. It is shown that the uncertain α-distribution-minimum spanning tree is just the uncertain expected minimum spanning tree when α = 0. For any α ∈ [0, 1], this problem can be transformed into an equivalent classical minimum spanning tree problem on a corresponding deterministic graph, which leads to effective algorithms with low computational complexity. Some numerical examples are presented as well to illustrate the performance of the proposed definitions and algorithm.