Fast Approximate Minimum Spanning Tree Algorithm Based on K-Means

It is difficult to apply traditional Minimum spanning tree(MST) algorithms to a large dataset since the time complexity of the algorithms is quadratic. In this paper, we present a fast approximate MST framework on the complete graph of N points, and any exact MST algorithm can be incorporated into the framework and speeded up. The proposed framework employs a divide-and-conquer scheme to produce an approximate MST with theoretical time complexity of O(N), if the incorporated exact MST algorithm has the running time of O(N). The framework consists of two stages. In the first stage, K-means is employed to partition a dataset into √ N clusters. Then an exact MST algorithm is applied to each cluster and the produced √ N MSTs are connected in terms of a proposed criterion to form an approximate MST. In the second stage, the clusters produced in the first stage form √ N − 1 neighboring pairs, and the dataset is repartitioned in order to make the neighboring boundaries of a neighboring pair be in the same cluster. Then another approximate MST is constructed. Finally, the two approximate MSTs are combined into a graph and a more accurate MST is generated from it. Experimental results show that the proposed approximate MST algorithm is computational efficient, and the approximation is sufficiently close to the true MST such that the performance in practical applications hardly suffers.