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Minimum spanning tree is a minimum-cost spanning tree connecting the whole network, but it couldn't be directly obtained on uncertain graph. In this paper, we define the reliability as the existence probability of all minimum spanning trees and present an algorithm for evaluating reliability of the minimum spanning tree on uncertain graph. The time complexity of the algorithm is O(Nmn), where n, m and N stand for the number of vertices, edges and minimum spanning trees, respectively. Because this algorithm spends more time finding minimum spanning tree, we propose an improved algorithm whose time complexity is O(Nm). The improved algorithm uses disjoint set data structure so that the average time complexity on finding a new minimum spanning tree is O(m/n). The two algorithms are analyzed in detail and the experiment results agree with theoretical analysis.

Reliability Evaluation of the Minimum Spanning Tree on Uncertain Graph