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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2018-04-01
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Online Access: | http://www.mdpi.com/1999-4893/11/4/53 |
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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 |
_version_ |
1716755309630849024 |