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

2000
*
SIAM journal on computing (Print)
*

We consider

doi:10.1137/s0097539796313477
fatcat:b4undpqm3jfj7nvfqmmlvkmwkq
*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. ...##
###
An improved algorithm for the maximum agreement subtree problem

2005
*
Information Processing Letters
*

In this paper, we solve

doi:10.1016/j.ipl.2005.02.005
fatcat:tphra5zngbh3hfziceszscnew4
*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. ...##
###
Balanced Randomized Tree Splitting with Applications to Evolutionary Tree Constructions
[chapter]

1999
*
Lecture Notes in Computer Science
*

approximation

doi:10.1007/3-540-49116-3_17
fatcat:w3eb5ii4uzexdn27iszfbxbhvi
*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 ...##
###
Kaikoura tree theorems: Computing the maximum agreement subtree

1993
*
Information Processing Letters
*

In this paper, we will present

doi:10.1016/0020-0190(93)90181-8
fatcat:7msydlipg5fc7eggqb4inxzh3q
*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. ...##
###
Rooted Maximum Agreement Supertrees
[chapter]

2004
*
Lecture Notes in Computer Science
*

Given a set T of rooted, unordered

doi:10.1007/978-3-540-24698-5_53
fatcat:d3yta7oxrfb7xf24wfhoqxa3xu
*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 . ...##
###
Rooted Maximum Agreement Supertrees

2005
*
Algorithmica
*

Given a set T of rooted, unordered

doi:10.1007/s00453-004-1147-5
fatcat:4jculpqzzfcnpk4obc4rcpulz4
*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 . ...##
###
Finding a Maximum Compatible Tree for a Bounded Number of Trees with Bounded Degree Is Solvable in Polynomial Time
[chapter]

2001
*
Lecture Notes in Computer Science
*

In this paper, we consider

doi:10.1007/3-540-44696-6_12
fatcat:bkubkrhczfe27ayjyeetofu7yu
*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*. ...##
###
An Even Faster and More Unifying Algorithm for Comparing Trees via Unbalanced Bipartite Matchings

2001
*
Journal of Algorithms
*

Based on these enhancements, we obtain

doi:10.1006/jagm.2001.1163
fatcat:urh6yo5n55bp3iwgjfrzdxrkwu
*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. ...##
###
An Even Faster and More Unifying Algorithm for Comparing Trees via Unbalanced Bipartite Matchings
[article]

2001
*
arXiv
*
pre-print

Based on these enhancements, we obtain

arXiv:cs/0101010v2
fatcat:eg3l3ipvq5cj7filmwk5y2fuim
*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. ...##
###
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

1997
*
SIAM journal on computing (Print)
*

We then show

doi:10.1137/s0097539794269461
fatcat:k45vlfhz4zgf7oobdbwun2q54e
*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. ...##
###
On the Extremal Maximum Agreement Subtree Problem
[article]

2018
*
arXiv
*
pre-print

Given two phylogenetic

arXiv:1812.06951v1
fatcat:phqya3h6nrhfhafjsayrrnccey
*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] ). ...##
###
Improved Parameterized Complexity of the Maximum Agreement Subtree and Maximum Compatible Tree Problems

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] . ...

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

2009
*
Discrete Applied Mathematics
*

This paper has been withdrawn by

doi:10.1016/j.dam.2008.06.007
fatcat:nj6jjtohwvc4roqfpkjrpju22a
*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). ...##
###
Online Consensus and Agreement of Phylogenetic Trees
[chapter]

2004
*
Lecture Notes in Computer Science
*

In this paper we present efficient online

doi:10.1007/978-3-540-30219-3_30
fatcat:st23urbytje75ilcgbm5vumuwi
*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. ...
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