Linking and Cutting Spanning Trees

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 outperf...

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Main Authors:	Luís M. S. Russo, Andreia Sofia Teixeira, Alexandre P. Francisco
Format:	Article
Language:	English
Published:	MDPI AG 2018-04-01
Series:	Algorithms
Subjects:	spanning tree uniform generation Markov chain mixing time link-cut tree
Online Access:	http://www.mdpi.com/1999-4893/11/4/53

id	doaj-11258eff00db4f25bc999e723f789051
record_format	Article
spelling	doaj-11258eff00db4f25bc999e723f7890512020-11-24T21:10:46ZengMDPI AGAlgorithms1999-48932018-04-011145310.3390/a11040053a11040053Linking and Cutting Spanning TreesLuís M. S. Russo0Andreia Sofia Teixeira1Alexandre P. Francisco2INESC-ID and the Department of Computer Science and Engineering, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa, PortugalINESC-ID and the Department of Computer Science and Engineering, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa, PortugalINESC-ID and the Department of Computer Science and Engineering, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa, PortugalWe 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.http://www.mdpi.com/1999-4893/11/4/53spanning treeuniform generationMarkov chainmixing timelink-cut tree
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Luís M. S. Russo Andreia Sofia Teixeira Alexandre P. Francisco
spellingShingle	Luís M. S. Russo Andreia Sofia Teixeira Alexandre P. Francisco Linking and Cutting Spanning Trees Algorithms spanning tree uniform generation Markov chain mixing time link-cut tree
author_facet	Luís M. S. Russo Andreia Sofia Teixeira Alexandre P. Francisco
author_sort	Luís M. S. Russo
title	Linking and Cutting Spanning Trees
title_short	Linking and Cutting Spanning Trees
title_full	Linking and Cutting Spanning Trees
title_fullStr	Linking and Cutting Spanning Trees
title_full_unstemmed	Linking and Cutting Spanning Trees
title_sort	linking and cutting spanning trees
publisher	MDPI AG
series	Algorithms
issn	1999-4893
publishDate	2018-04-01
description	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.
topic	spanning tree uniform generation Markov chain mixing time link-cut tree
url	http://www.mdpi.com/1999-4893/11/4/53
work_keys_str_mv	AT luismsrusso linkingandcuttingspanningtrees AT andreiasofiateixeira linkingandcuttingspanningtrees AT alexandrepfrancisco linkingandcuttingspanningtrees
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Linking and Cutting Spanning Trees

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