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Algorithms 2018, 11(4), 53; https://doi.org/10.3390/a11040053

Linking and Cutting Spanning Trees

INESC-ID and the Department of Computer Science and Engineering, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal
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Received: 12 March 2018 / Revised: 11 April 2018 / Accepted: 11 April 2018 / Published: 19 April 2018
(This article belongs to the Special Issue Efficient Data Structures)

Abstract

We consider the problem of uniformly generating a spanning tree for an undirected connected graph. This process is useful for computing 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, experimental results show that the chain converges quickly. This yields an efficient algorithm due to the use of proper fast data structures. To obtain the mixing time of the chain we describe a coupling, which we analyze for cycle graphs and simulate for other graphs. View Full-Text
Keywords: spanning tree; uniform generation; Markov chain; mixing time; link-cut tree spanning tree; uniform generation; Markov chain; mixing time; link-cut tree
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Russo, L.M.S.; Teixeira, A.S.; Francisco, A.P. Linking and Cutting Spanning Trees. Algorithms 2018, 11, 53.

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