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An O(nlog n) Algorithm for the Maximum Agreement Subtree Problem for Binary Trees

Richard Cole, Martin Farach-Colton, Ramesh Hariharan, Teresa Przytycka, Mikkel Thorup
2000 SIAM journal on computing (Print)  
We consider the case which occurs frequently in practice, i.e., the case when the trees are binary, and give an O(n log n) time algorithm for this problem.  ...  The maximum agreement subtree problem is the following.  ...  We would like to thank the referees for some very thorough comments.  ... 
doi:10.1137/s0097539796313477 fatcat:b4undpqm3jfj7nvfqmmlvkmwkq

An improved algorithm for the maximum agreement subtree problem

Chuan-Min Lee, Ling-Ju Hung, Maw-Shang Chang, Chia-Ben Shen, Chuan-Yi Tang
2005 Information Processing Letters  
In this paper, we solve the maximum agreement subtree problem for a set T of k rooted leaf-labeled evolutionary trees on n leaves where T contains a binary tree.  ...  For k = 3, it yields the best known algorithm which runs in O(n 2 log n log log n)-time.  ...  Acknowledgement We would like to thank the anonymous referees for their helpful comments and suggestions which considerately improved the presentation of the paper.  ... 
doi:10.1016/j.ipl.2005.02.005 fatcat:tphra5zngbh3hfziceszscnew4

Balanced Randomized Tree Splitting with Applications to Evolutionary Tree Constructions [chapter]

Ming-Yang Kao, Andrzej Lingas, Anna Östlin
1999 Lecture Notes in Computer Science  
approximation algorithm for the maximum agreement subtree problem for binary trees for which the maximum number of leaves in an optimal solution is large.  ...  We also present new lower bounds for the problem of constructing an evolutionary tree from experiments and for the problem of constructing a tree from an ultrametric distance matrix. a b d d c a a d f  ...  For trees not restricted to be binary Kannan et al. present an O(n 2 )-time algorithm, which performs O(dn log n) experiments, where d is the maximum degree in the tree, and for the unrestricted degree  ... 
doi:10.1007/3-540-49116-3_17 fatcat:w3eb5ii4uzexdn27iszfbxbhvi

Kaikoura tree theorems: Computing the maximum agreement subtree

Mike Steel, Tandy Warnow
1993 Information Processing Letters  
In this paper, we will present an 0(n4.5 log IZ + V> algorithm to determine the largest agreement subtree of two trees on n leaves, where V is the maximum number of nodes in the trees.  ...  For the case of trees of maximum degree k, there are two algorithms presented: one has running time 0(k!n2 + V) while the other has running time O(k2%z2 log n + V).  ...  Acknowledgements The authors wish to thank NSF for providing funds for the second author to travel to New Zealand and work with the first author.  ... 
doi:10.1016/0020-0190(93)90181-8 fatcat:7msydlipg5fc7eggqb4inxzh3q

Rooted Maximum Agreement Supertrees [chapter]

Jesper Jansson, Joseph H. -K. Ng, Kunihiko Sadakane, Wing-Kin Sung
2004 Lecture Notes in Computer Science  
Given a set T of rooted, unordered trees, where each Ti ∈ T is distinctly leaf-labeled by a set Λ(Ti) and where the sets Λ(Ti) may overlap, the maximum agreement supertree problem (MASP) is to construct  ...  We then present an algorithm for MASP with D = 2 whose running time is polynomial if k = O(1).  ...  The maximum agreement subtree problem (MAST), also referred to in the literature as the maximum homeomorphic subtree problem (MHT), is to find a maximum agreement subtree of T .  ... 
doi:10.1007/978-3-540-24698-5_53 fatcat:d3yta7oxrfb7xf24wfhoqxa3xu

Rooted Maximum Agreement Supertrees

Jesper Jansson, Joseph H.-K. Ng, Kunihiko Sadakane, Wing-Kin Sung
2005 Algorithmica  
Given a set T of rooted, unordered trees, where each Ti ∈ T is distinctly leaf-labeled by a set Λ(Ti) and where the sets Λ(Ti) may overlap, the maximum agreement supertree problem (MASP) is to construct  ...  We then present an algorithm for MASP with D = 2 whose running time is polynomial if k = O(1).  ...  The maximum agreement subtree problem (MAST), also referred to in the literature as the maximum homeomorphic subtree problem (MHT), is to find a maximum agreement subtree of T .  ... 
doi:10.1007/s00453-004-1147-5 fatcat:4jculpqzzfcnpk4obc4rcpulz4

Finding a Maximum Compatible Tree for a Bounded Number of Trees with Bounded Degree Is Solvable in Polynomial Time [chapter]

Ganeshkumar Ganapathysaravanabavan, Tandy Warnow
2001 Lecture Notes in Computer Science  
In this paper, we consider the problem of computing a maximum compatible tree for k rooted trees when the maximum degree of all trees is bounded.  ...  Hence, a maximum compatible tree for k unrooted trees can be found in in O£ 2 2kd n k¥ 1 ¤ time.  ...  Our result for the MCS problem is an algorithm for the two-tree MCS problem which runs in time O¦ 2 4d n 3 § time, where n© S © a nd d is the maximum degree of the two unrooted trees.  ... 
doi:10.1007/3-540-44696-6_12 fatcat:bkubkrhczfe27ayjyeetofu7yu

An Even Faster and More Unifying Algorithm for Comparing Trees via Unbalanced Bipartite Matchings

Ming-Yang Kao, Tak-Wah Lam, Wing-Kin Sung, Hing-Fung Ting
2001 Journal of Algorithms  
Based on these enhancements, we obtain an efficient algorithm for a new matching problem called the hierarchical bipartite matching problem, which is at the core of our maximum agreement subtree algorithm  ...  A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees.  ...  Acknowledgments We wish to thank anonymous referees for extremely helpful suggestions.  ... 
doi:10.1006/jagm.2001.1163 fatcat:urh6yo5n55bp3iwgjfrzdxrkwu

An Even Faster and More Unifying Algorithm for Comparing Trees via Unbalanced Bipartite Matchings [article]

Ming-Yang Kao, Tak-Wah Lam, Wing-Kin Sung, Hing-Fung Ting
2001 arXiv   pre-print
Based on these enhancements, we obtain an efficient algorithm for a new matching problem called the hierarchical bipartite matching problem, which is at the core of our maximum agreement subtree algorithm  ...  A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees.  ...  Acknowledgments We wish to thank anonymous referees for extremely helpful suggestions.  ... 
arXiv:cs/0101010v2 fatcat:eg3l3ipvq5cj7filmwk5y2fuim

Page 2367 of Mathematical Reviews Vol. , Issue 95d [page]

1995 Mathematical Reviews  
In this paper, we present an O(n*>logn+V) algorithm for determining the largest agreement subtree of two trees on n leaves, where V is the maximum number of nodes in the trees.  ...  For the case of trees with maximum degree k, two algorithms are presented: one has running time O(k!n? + V) and the other has running time O(k?°n? logn + V).  ... 

Maximum Agreement Subtree in a Set of Evolutionary Trees: Metrics and Efficient Algorithms

Amihood Amir, Dmitry Keselman
1997 SIAM journal on computing (Print)  
We then show an approximation algorithm of time O( kn5) for choosing the species that are not in a maximum agreement subtree of a set of k trees.  ...  In this paper we prove that the maximum homeomorphic agreement subtree problem is NP-complete for three trees with unbounded degrees.  ...  Acknowledgements We wish to thank Mike Steel for his great help in refining this paper, and Bob Robinson for kindly sending us reference material on the subject.  ... 
doi:10.1137/s0097539794269461 fatcat:k45vlfhz4zgf7oobdbwun2q54e

On the Extremal Maximum Agreement Subtree Problem [article]

Alexey Markin
2018 arXiv   pre-print
Given two phylogenetic trees with the {1, ..., n} leaf-set the maximum agreement subtree problem asks what is the maximum size of the subset A ⊆{1, ..., n} such that the two trees are equivalent when restricted  ...  The long-standing extremal version of this problem focuses on the smallest number of leaves, mast(n), on which any two (binary and unrooted) phylogenetic trees with n leaves must agree.  ...  Introduction The algorithmic aspects of the maximum agreement subtree problem have been heavily researched for many versions of this problem (see, e.g., [1, 2, 7] ).  ... 
arXiv:1812.06951v1 fatcat:phqya3h6nrhfhafjsayrrnccey

Improved Parameterized Complexity of the Maximum Agreement Subtree and Maximum Compatible Tree Problems

V. Berry, F. Nicolas
2006 IEEE/ACM Transactions on Computational Biology & Bioinformatics  
The authors are also grateful to anonymous reviewers for their valuable comments.  ...  Acknowledgement The authors thank C. Paul and J. Cassaigne for careful readings of the manuscript and help in simplifying some proofs.  ...  Efficient polynomial time algorithms have been recently proposed for MAST on two rooted n-leaf trees: O(n log n) for binary trees [6] , and O( √ dn log 2n d ) for trees of degree bounded by d [5] .  ... 
doi:10.1109/tcbb.2006.39 pmid:17048466 fatcat:kgzvgwsosbdipam4vzx3wqkoma

On the approximability of the Maximum Agreement SubTree and Maximum Compatible Tree problems

Sylvain Guillemot, François Nicolas, Vincent Berry, Christophe Paul
2009 Discrete Applied Mathematics  
This paper has been withdrawn by the corresponding author because the newest version is now published in Discrete Applied Mathematics.  ...  Acknowledgments The authors thank anonymous journal reviewers for helpful comments.  ...  François Nicolas was supported by the Academy of Finland under grant 204785 (Automata Theory and Combinatorics on Words).  ... 
doi:10.1016/j.dam.2008.06.007 fatcat:nj6jjtohwvc4roqfpkjrpju22a

Online Consensus and Agreement of Phylogenetic Trees [chapter]

Tanya Y. Berger-Wolf
2004 Lecture Notes in Computer Science  
In this paper we present efficient online algorithms for computing strict and majority consensi and the maximum agreement subtree.  ...  Consensus and agreement trees are common such representations. Using existing static algorithms to produce these trees increases an already lengthy computational time substantially.  ...  The author is deeply grateful to Tandy Warnow for suggesting the problem and for many insights.  ... 
doi:10.1007/978-3-540-30219-3_30 fatcat:st23urbytje75ilcgbm5vumuwi
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