Linking and Cutting Spanning Trees
Abstract
We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle graphs we prove that this approach significantly outperforms existing algorithms. For general graphs we obtain no analytical bounds, but experimental results show that the chain still converges quickly. This yields an efficient algorithm, also due to the use of proper fast data structures. To bound the mixing time of the chain we describe a coupling, which we analyse for cycle graphs and simulate for other graphs.
Keywords
Cite
@article{arxiv.1801.06846,
title = {Linking and Cutting Spanning Trees},
author = {Luís M. S. Russo and Andreia Sofia Teixeira and Alexandre P Francisco},
journal= {arXiv preprint arXiv:1801.06846},
year = {2020}
}
Comments
This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 690941. Prototype implementation at https://github.com/LuisRusso-INESC-ID/LinkCutSpanningTrees