Fast Generation of Random Spanning Trees and the Effective Resistance Metric

@inproceedings{Madry2015FastGO,
  title={Fast Generation of Random Spanning Trees and the Effective Resistance Metric},
  author={Aleksander Madry and Damian Straszak and Jakub Tarnawski},
  booktitle={ACM-SIAM Symposium on Discrete Algorithms},
  year={2015}
}
We present a new algorithm for generating a uniformly random spanning tree in an undirected graph. Our algorithm samples such a tree in expected $\tilde{O}(m^{4/3})$ time. This improves over the best previously known bound of $\min(\tilde{O}(m\sqrt{n}),O(n^{\omega}))$ -- that follows from the work of Kelner and M\k{a}dry [FOCS'09] and of Colbourn et al. [J. Algorithms'96] -- whenever the input graph is sufficiently sparse. At a high level, our result stems from carefully exploiting the… 

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