# Generating random spanning trees more quickly than the cover time

@inproceedings{Wilson1996GeneratingRS, title={Generating random spanning trees more quickly than the cover time}, author={David Bruce Wilson}, booktitle={STOC '96}, year={1996} }

It is widely known how to generate random spanning trees of an undirected graph. Broder showed how at FOCS [6], and Aldous too found the algorithm [2]. Start at any vertex and do a simple random walk on the graph. Each time a vertex is first encountered, mark the edge from which it was discovered. When all the vertices are discovered, the marked edges form a random spanning tree. This algorithm is easy to code up, has small running time constants, and has a nice proof that it generates trees…

## 458 Citations

An almost-linear time algorithm for uniform random spanning tree generation

- Mathematics, Computer ScienceSTOC
- 2018

An m1+o(1)βo( 1)-time algorithm for generating uniformly random spanning trees in weighted graphs with max-to-min weight ratio β is given and it is shown that most random walk steps occur far away from an unvisited vertex.

Generating Random Spanning Trees via Fast Matrix Multiplication

- Computer Science, MathematicsLATIN
- 2016

The best algorithm for dense graphs can produce a uniformly random spanning tree of an n-vertex graph in time \(O(n^{2.38})\).

Faster generation of random spanning trees by Aleksander M 4 dry

- Computer Science, Mathematics
- 2010

A new algorithm for generating approximately uniformly random spanning trees in undirected graphs by exploiting the connection between random walks on graphs and electrical networks is introduced to introduce a new approach to the problem that integrates discrete random walk-based techniques with continuous linear algebraic methods.

Sampling random spanning trees faster than matrix multiplication

- Computer Science, MathematicsSTOC
- 2017

An algorithm is presented that, with high probability, generates a random spanning tree from an edge-weighted undirected graph in (n5/3 m1/3) time, based on Gaussian elimination, and the fact that effective resistance is preserved in the graph resulting from eliminating a subset of vertices (called a Schur complement).

Random spanning forests, Markov matrix spectra and well distributed points

- Mathematics
- 2014

This paper is a variation on the uniform spanning tree theme. We use random spanning forests to solve the following problem: for a Markov process on a finite set of size n, find a probability law on…

PR ] 2 4 Ju l 2 01 9 A Reverse Aldous / Broder Algorithm

- Mathematics
- 2019

The Aldous/Broder algorithm provides a way of sampling a uniform spanning tree for finite connected graphs using simple random walk. Namely, start a simple random walk on a connected graph and stop…

Generating a Random Sink-free Orientation in Quadratic Time

- MathematicsElectron. J. Comb.
- 2002

A simple randomized algorithm inspired by Wilson's cycle popping method is presented which obtains an exact sample in mean time at most $O(nm)$, where $n$ is the number of vertices.

Distributed Random Walks

- Computer Science, MathematicsJACM
- 2013

A sublinear time distributed algorithm for performing random walks whose time complexity is sublinear in the length of the walk and which is fully decentralized and can serve as a building block in the design of topologically-aware networks.

Two Applications of Random Spanning Forests

- Mathematics
- 2018

We use random spanning forests to find, for any Markov process on a finite set of size n and any positive integer $$m \le n$$m≤n, a probability law on the subsets of size m such that the mean hitting…

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