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Computing the Edit-Distance Between Unrooted Ordered Trees [chapter]

Philip N. Klein
1998 Lecture Notes in Computer Science  
We give an O(n 3 log n) algorithm to compute the edit distance between two ordered trees.  ...  The edit distance between A and B is the minimum cost of a sequence of operations (contract an edge, uncontract an edge, modify the label of an edge) needed to transform A into B.  ...  One might consider generalizing from edit-distance between ordered trees to edit-distance between planar graphs.  ... 
doi:10.1007/3-540-68530-8_8 fatcat:tfr7lfnyqbd55fpvppfkdprcue

Edit Distance between Unrooted Trees in Cubic Time

Bartlomiej Dudek, Pawel Gawrychowski, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
We show that this is, in fact, not the case, and edit distance between unrooted trees on n nodes can be computed in O(n 3 ) time.  ...  [ACM Trans. on Algorithms, 6(1), 2009] showed how to compute the edit distance between rooted trees on n nodes in O(n 3 ) time.  ...  Second structure of RNA can be modeled as an ordered tree [17, 26] , so we would like to generalize computing the edit distance between strings to computing the edit distance between ordered trees.  ... 
doi:10.4230/lipics.icalp.2018.45 dblp:conf/icalp/DudekG18 fatcat:6e3g5otx65al7dem7efx6senq4

A Polynomial-Time Metric for Attributed Trees [chapter]

Andrea Torsello, Džena Hidović, Marcello Pelillo
2004 Lecture Notes in Computer Science  
This is a remarkable and attractive property since the computation of traditional edit-distance-based metrics is NP-complete, except for ordered structures.  ...  The proposed measure is general and defined on trees endowed with either symbolic or continuous-valued attributes, and can be equally applied to ordered and unordered, rooted and unrooted trees.  ...  Since edit-distance on ordered trees can be computed in polynomial time, in the paper we focus on the unordered case where our approach provides a clear computational advantage.  ... 
doi:10.1007/978-3-540-24673-2_34 fatcat:yjsoyhraozfcvn7vcugrd6zetq

[Inside back cover]

2005 IEEE Transactions on Pattern Analysis and Machine Intelligence  
This is a remarkable and attractive property since the computation of traditional edit-distance-based metrics is NP-complete, except for ordered structures.  ...  The proposed measure is general and defined on trees endowed with either symbolic or continuous-valued attributes, and can be equally applied to ordered and unordered, rooted and unrooted trees.  ...  Since edit-distance on ordered trees can be computed in polynomial time, in the paper we focus on the unordered case where our approach provides a clear computational advantage.  ... 
doi:10.1109/tpami.2005.136 pmid:16013756 fatcat:jga4j63mmfhx7ib2efxzxnktdu

Edit Distance between Unrooted Trees in Cubic Time [article]

Bartłomiej Dudek, Paweł Gawrychowski
2018 arXiv   pre-print
We show that this is, in fact, not the case, and edit distance between unrooted trees on $n$ nodes can be computed in $\mathcal{O}(n^{3})$ time.  ...  [ACM Trans. on Algorithms, 6(1), 2009] showed how to compute the edit distance between rooted trees on $n$ nodes in $\mathcal{O}(n^{3})$ time.  ...  Second structure of RNA can be modeled as an ordered tree [17, 26] , so we would like to generalize computing the edit distance between strings to computing the edit distance between ordered trees.  ... 
arXiv:1804.10186v1 fatcat:win5ethcfnfz5aaqqljgarq6vi

Comparing reconciled gene trees in linear time

Céline Scornavacca
2020 Peer Community In Mathematical and Computational Biology  
In the present paper [6], the authors introduce a distance called LRF, which is inspired by the TED (Tree Edit Distance [7]) and is based on node edits.  ...  This distance, called ELRF, is based on edge edits and coincides with the RF distance when all internal labels are identical; unfortunately, the ELRF distance is very costly to compute.  ...  The authors show the pertinence of this new distance by studying the impact of taxon sampling on reconciled gene trees when internal labels are computed via a method based on species overlap.  ... 
doi:10.24072/pci.mcb.100002 fatcat:ilj34jz7ljfhjfxmzr24fbrqxe

RNA Tree Comparisons via Unrooted Unordered Alignments [chapter]

Nimrod Milo, Shay Zakov, Erez Katzenelson, Eitan Bachmat, Yefim Dinitz, Michal Ziv-Ukelson
2012 Lecture Notes in Computer Science  
Several variants of tree edit distance and alignment problems were previously studied.  ...  These variants differ in the type of trees they examine (ordered/unordered, rooted/unrooted), and in the type of edit operations or alignment restrictions they apply [8] .  ...  This research was partially supported by ISF grant 478/10 and by the Frankel Center for Computer Science at Ben Gurion University of the Negev.  ... 
doi:10.1007/978-3-642-33122-0_11 fatcat:r2p7okgv4zflvduiphdh66gueu

Fast Local Search for Unrooted Robinson-Foulds Supertrees [chapter]

Ruchi Chaudhary, J. Gordon Burleigh, David Fernández-Baca
2011 Lecture Notes in Computer Science  
This simplifies the algorithm considerably and allows us to compute RF distances without restricting the supertree to the leaf set of each input tree.  ...  Fast Local Search for Unrooted Robinson-Foulds Supertrees 185 edit operation.  ...  J.G.B. was supported in part by the NIMBioS Gene Tree Reconciliation Working Group, through NSF grant EF-0832858, with additional support from the University of Tennessee.  ... 
doi:10.1007/978-3-642-21260-4_20 fatcat:65mgtbuhcvervm3y6rcrdrikj4

Polynomial-time metrics for attributed trees

A. Torsello, D. Hidovic-Rowe, M. Pelillo
2005 IEEE Transactions on Pattern Analysis and Machine Intelligence  
This is a remarkable and attractive property, since the computation of traditional edit-distance-based metrics is NP-complete, except for ordered structures.  ...  The proposed measures are general and defined on trees endowed with either symbolic or continuous-valued attributes, and can be equally applied to ordered and unordered, rooted and unrooted trees.  ...  Since edit-distance on ordered trees can be computed in polynomial time, in the paper we focus on the unordered case where our approach provides a clear computational advantage.  ... 
doi:10.1109/tpami.2005.146 pmid:16013756 fatcat:s3svzn2uhnecxh5t7zqnwqfds4

Phylogenetic identification of lateral genetic transfer events

Robert G Beiko, Nicholas Hamilton
2006 BMC Evolutionary Biology  
rooted trees, and may be so for unrooted trees as well.  ...  , suggesting that real transfer events occur most frequently between closely related organisms, but can span large phylogenetic distances as well.  ...  Computing facilities were provided by the Australian Partnership in Advanced Computing and Queensland Parallel Supercomputing Foundation.  ... 
doi:10.1186/1471-2148-6-15 pmid:16472400 pmcid:PMC1431587 fatcat:fh7jjs3omjfo3bhn3zt4jl3qgy

Recent Results on Three Problems in Comparative Structural RNAomics

Shay Zakov, Nimrod Milo, Tamar Pinhas, Sivan Yogev, Erez Katzenelson, Eitan Bachmat, Yefim Dinitz, Dekel Tsur, Michal Ziv-Ukelson, Fabrice Jossinet, Michal Ziv-Ukelson, Yann Ponty (+1 others)
2014 European Conference on Computational Biology  
Our contribution includes: (1) a new worst-case bound for Discrete RNA Folding, (2) Unordered Unrooted Comparisons of RNA Trees, and (3) an RNA Homology Search where the query is an RNA sequence and the  ...  A common denominator of these three works is that they demonstrate research problems tackled within current structural RNAomics, whose solution extends to more general classical problems in Computer Science  ...  Due to NP hardness of general Unordered Tree Edit Distance, we define a Homeomorphic Subtree Alignment variant, in which only nodes of degree 2 (or whole subtrees) can be deleted from both trees [2] .  ... 
doi:10.15455/cmsr.2014.0005 dblp:conf/eccb/ZakovMPYKBDTZ14 fatcat:njpwkdycqzdfta4uqe7vsbqtku

TreeCmp: Comparison of Trees in Polynomial Time

Damian Bogdanowicz, Krzysztof Giaro, Borys Wróbel
2012 Evolutionary Bioinformatics  
similarity between trees.  ...  When a phylogenetic reconstruction does not result in one tree but in several, tree metrics permit finding out how far the reconstructed trees are from one another.  ...  Acknowledgements We would like to thank Morgan Price for the dataset of alignments and trees.  ... 
doi:10.4137/ebo.s9657 fatcat:kso5lkb7ffcqlkeipgbq244mve

Homeomorphic alignment of weighted trees

Benjamin Raynal, Michel Couprie, Venceslas Biri
2010 Pattern Recognition  
To solve this problem, we propose a new alignment, taking into account the homeomorphism between trees, rather than the isomorphism, as in prior works.  ...  For this purpose, we match the tree representation of the skeleton of the 3D shape to a pre-specified tree model.  ...  Algorithm for unrooted trees First, let us give an expression of the homeomorphic alignment distance between unrooted trees, in function of the distances between all their possible rooted versions.  ... 
doi:10.1016/j.patcog.2010.03.015 fatcat:3vbmcjxhknf6jbev66xpope7aa

A generalized Robinson-Foulds distance for labeled trees

Samuel Briand, Christophe Dessimoz, Nadia El-Mabrouk, Manuel Lafond, Gabriela Lobinska
2020 BMC Genomics  
Background The Robinson-Foulds (RF) distance is a well-established measure between phylogenetic trees.  ...  In particular, we show that contrary to the unlabeled case, an optimal edit path may require contracting "good" edges, i.e. edges shared between the two trees.  ...  Acknowledgements The authors thank the Program Committee of APBC2020 for the three constructive peer-reviews. About this supplement  ... 
doi:10.1186/s12864-020-07011-0 pmid:33208096 pmcid:PMC7677779 fatcat:xcwa2hvyijaizk2gk7ygy24y4a

The Bourque distances for mutation trees of cancers

Katharina Jahn, Niko Beerenwinkel, Louxin Zhang
2021 Algorithms for Molecular Biology  
We show the basic version of the Bourque distance for mutation trees can be computed in linear time.  ...  We also make a connection between the Robinson–Foulds distance and the nearest neighbor interchange distance.  ...  Acknowledgements LXZ thanks Gabriel Valiente for helpful comments on the conference version of this work.  ... 
doi:10.1186/s13015-021-00188-3 pmid:34112201 fatcat:s5i6jze6wngqnimzar64ruuozm
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