# An optimal minimum spanning tree algorithm

@inproceedings{Pettie2002AnOM, title={An optimal minimum spanning tree algorithm}, author={Seth Pettie and Vijaya Ramachandran}, booktitle={JACM}, year={2002} }

We establish that the algorithmic complexity of the minimumspanning tree problem is equal to its decision-tree complexity.Specifically, we present a deterministic algorithm to find aminimum spanning tree of a graph with <i>n</i> vertices and<i>m</i> edges that runs in time<i>O</i>(<i>T</i><sup>*</sup>(<i>m,n</i>)) where<i>T</i><sup>*</sup> is the minimum number of edge-weightcomparisons needed to determine the solution. The algorithm isquite simple and can be implemented on a pointer machine…

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