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Binary subtrees with few labeled paths

2011
*
Combinatorica
*

We prove several quantitative Ramseyan results involving ternary complete trees

doi:10.1007/s00493-011-2634-3
fatcat:lg5lvzl6ufd6pdi2nlfweebi4m
*with*{0, 1}-*labeled*edges where we attempt to find a complete*binary**subtree**with*as*few**labels*as possible along its*paths*... So the key for this process is arguing not only that given a single edge-*labeled*ternary tree we can find a complete*binary**subtree**with**few**path*-*labels*, but actually that given a family of edge-*labeled*... Corollary 3.2 gives some control over the*path*-*labels*that appear in the*binary**subtrees*. ...##
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Smirnov Trees

2019
*
Electronic Journal of Combinatorics
*

We introduce a generalization of Smirnov words in the context of

doi:10.37236/8484
fatcat:hlwgrjo3trajzp7aiqj75fcb5m
*labeled**binary*trees, which we call Smirnov trees. ... If, on the other hand, γ is the first node on the principal*path*of β's parent's right*subtree**with**label*b and S is the*subtree*of T*with*root γ, then T = Φ(T \ S, S, b). ... M < b), or a > b and b is smaller than all the*labels*on the principal*path*(i.e. m > b), create a new root*with**label*b,*with*no right child, and*with*the entire T as its left*subtree*. ...##
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Smirnov Trees
[article]

2019
*
arXiv
*
pre-print

We introduce a generalization of Smirnov words in the context of

arXiv:1901.10140v1
fatcat:ekbj3ki27vewdi5h2dlgtqvtk4
*labeled**binary*trees, which we call Smirnov trees. ... If, on the other hand, γ is the first node on the principal*path*of β's parent's right*subtree**with**label*≥ b and S is the*subtree*of T*with*root γ, then T = Φ(T \ S, S, b). ... M < b), or a > b and b is smaller than all the*labels*on the principal*path*(i.e. m > b), create a new root*with**label*b,*with*no right child, and*with*the entire T as its left*subtree*. ...##
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Defining binary phylogenetic trees using parsimony
[article]

2021
*
arXiv
*
pre-print

It is generally assumed that this criterion works well for data

arXiv:2111.04385v1
fatcat:dlwc3bztaffufg4koemi6zw7ky
*with*only*few*underlying changes. ... Phylogenetic (i.e. leaf-*labeled*) trees play a fundamental role in evolutionary research. ... Recall that we*labeled*all taxa in A*with*a and x 1 and x 2 were*labeled*b. ...##
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Nearly optimal binary search trees

1975
*
Acta Informatica
*

Therefore we define the weighted

doi:10.1007/bf00264563
fatcat:xzg7pz4babcorci36nheiombqi
*path*length of tree T as: Knuth [4] gives an algorithm for constructing an optimum*binary*search tree, i.e. a tree*with*minimal weighted*path*length. ... A*binary*search tree T is a tree*with*n interior nodes (nodes having two sons), which we denote by circles, and n+ t leaves, which we denote by squares. ... Fig. 4 .. 4 The Let T be a*binary*tree which is constructed according to Rule II and let B be an interior node*with*distance b from the root. Let w be the total weight of the*subtree**with*root B. ...##
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Functional Pearls

1996
*
Journal of functional programming
*

*Binary*trees Finally, we come to

*binary*trees. The type btree A consists of

*binary*trees

*labelled*

*with*elements of type A. ... A

*binary*tree is either a leaf // a

*labelled*

*with*a single element a, or a branch br {t,a,u) consisting of two children t and u and a

*label*a. ...

##
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On the Complexity of Duplication-Transfer-Loss Reconciliation with Non-binary Gene Trees
[chapter]

2015
*
Lecture Notes in Computer Science
*

*With*such non-

*binary*gene trees, the reconciliation problem seeks to find a

*binary*resolution of the gene tree that minimizes the reconciliation cost. ... Yet, no efficient algorithms exist for DTL reconciliation

*with*non-

*binary*gene trees and the complexity of the problem remains unknown. ... Thus, all the g i 's (along

*with*g ′ i 's and g ′′ i 's) must map to as

*few*of the

*subtrees*, S(s j )'s, as possible. ...

##
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Optimal tree access by elementary and composite templates in parallel memory systems

2002
*
IEEE Transactions on Parallel and Distributed Systems
*

complete

doi:10.1109/71.995820
fatcat:r7lu5ezw3za7vnfzwl7q3f6iby
*subtrees*of size K and*paths*of size N such that N K À dlog Ke M; 2) at most I conflict in accessing complete*subtrees*and*paths*of size M; 3) O K M c À Á conflicts when accessing a composite ... template of K nodes consisting of c disjoint subsets, each subset being a complete*subtree*, or a*path*or a set of consecutive nodes in a level of the tree. ... accessing*paths*of each*subtree*and a*few*conflicts occurs on levels. ...##
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Algorithms for Computing Cluster Dissimilarity between Rooted Phylogenetic Trees

2015
*
Open Cybernetics and Systemics Journal
*

Each vertex of a rooted tree associates

doi:10.2174/1874110x01509012218
fatcat:skuhz2obkvaldnkiujv3pitadm
*with*a cluster, i.e., the subset of leaf*labels*in the*subtree*rooted at this vertex. ... Each vertex u of T associates*with*a cluster denoted by ( ) L u , i.e., the set of leaf*labels*in the*subtree*rooted at u . ...##
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An O(nlog n) Algorithm for the Maximum Agreement Subtree Problem for Binary Trees

2000
*
SIAM journal on computing (Print)
*

The maximum agreement

doi:10.1137/s0097539796313477
fatcat:b4undpqm3jfj7nvfqmmlvkmwkq
*subtree*problem is the following. ... 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 leaves in each tree are*labeled**with*the same set of*labels*, and further, no*label*occurs more than once in a particular tree. An agreement*subtree*of T 1 and T 2 is defined as follows. ...##
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Maximum Covering Subtrees for Phylogenetic Networks
[article]

2020
*
arXiv
*
pre-print

Tree-based phylogenetic networks, which may be roughly defined as leaf-

arXiv:2009.12413v2
fatcat:74rlqlhorffqrbliecaqeldn7m
*labeled*networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories ... We answer an open question of Francis, Semple, and Steel about the complexity of determining how far a phylogenetic network is from being tree-based, including non-*binary*phylogenetic networks. ... We formalize the problem as: Maximum Covering*Subtree*(MAX-CST) INSTANCE: A leaf-*labeled*network N = (V, A, L, ρ)*with*vertices V , directed edges A, leaves L, and root ρ. ...##
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Better Labeling Schemes for Nearest Common Ancestors through Minor-Universal Trees
[article]

2017
*
arXiv
*
pre-print

A

arXiv:1707.06011v1
fatcat:kspnjaz3cvd3zdu6nl5ngh33ia
*labeling*scheme for nearest common ancestors assigns a distinct*binary*string, called the*label*, to every node of a tree, so that given the*labels*of two nodes (and no further information about the topology ... We complement the existential results*with*a generic transformation that decreases the query time to constant in any scheme based on a minor-universal tree. ... [9] (and also all previous schemes) is based on the notion of heavy*path*decomposition. For every heavy*path*, we assign a*binary*code to the root of each*subtree*hanging off it. ...##
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TWIX

2006
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Proceedings of the 1st international conference on Scalable information systems - InfoScale '06
*

*labeling*and tree traversal algorithm. ... propose a novel technique for matching XML twig query patterns, named TWIX, which results in a substantial reduction of the search space, response time, size and structure invariance through a distributed

*binary*... It is constructed using the

*binary*

*labels*associated

*with*each leaf instance node of a matching instance pair. ...

##
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Labeling Schemes for Nearest Common Ancestors through Minor-Universal Trees
[chapter]

2018
*
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
*

Syst. 37(3):441-456 2004] showed that O(log n)-bit

doi:10.1137/1.9781611975031.166
dblp:conf/soda/GawrychowskiKLP18
fatcat:u7c3fhruz5ga5ejhsopneqfjgq
*labels*are enough,*with*a somewhat large constant. ... Quite a*few*linear-space constant-time solutions are known and the problem seems to be well-understood. This is however not so clear if we want to design a*labeling*scheme. ... All existing NCA*labeling*schemes are based on some version of this notion and assigning variable length codes to the roots of all*subtrees*hanging off the heavy*path*, so that larger*subtrees*receive shorter ...##
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Efficient Dynamic Embeddings of Binary Trees into Hypercubes

2002
*
Journal of Algorithms
*

In this paper, a deterministic algorithm for dynamically embedding

doi:10.1006/jagm.2002.1218
fatcat:aq7ibim4jzfl3e73n2auoxtx2i
*binary*trees into hypercubes is presented. ... ., remapping of tree vertices, to obtain an embedding of trees into hypercubes*with*small dilation, load, and expansion simultaneously. ... Next, if v has a right child, link Lower(v)*with*the beginning of the Euler contour*path*of its right*subtree*and link the end of this Euler contour*path**with*Right(v), and link Lower(v)*with*Right( ...
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