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LATIN
2016
Springer

Generating Random Spanning Trees via Fast Matrix Multiplication

2 years 11 months ago
Generating Random Spanning Trees via Fast Matrix Multiplication
We consider the problem of sampling a uniformly random spanning tree of a graph. This is a classic algorithmic problem for which several exact and approximate algorithms are known. Random spanning trees have several connections to Laplacian matrices; this leads to algorithms based on fast matrix multiplication. The best algorithm for dense graphs can produce a uniformly random spanning tree of an nvertex graph in time O(n2.38 ). This algorithm is intricate and requires explicitly computing the LU-decomposition of the Laplacian. We present a new algorithm that also runs in time O(n2.38 ) but has several conceptual advantages. First, whereas previous algorithms need to introduce directed graphs, our algorithm works only with undirected graphs. Second, our algorithm uses fast matrix inversion as a black-box, thereby avoiding the intricate details of the LU-decomposition.
Nicholas J. A. Harvey, Keyulu Xu
Added 07 Apr 2016
Updated 07 Apr 2016
Type Journal
Year 2016
Where LATIN
Authors Nicholas J. A. Harvey, Keyulu Xu
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