Filters

11,863 Hits in 3.8 sec

### Binary subtrees with few labeled paths

Rodney G. Downey, Noam Greenberg, Carl G. Jockusch, Kevin G. Milans
2011 Combinatorica
We prove several quantitative Ramseyan results involving ternary complete trees 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.  ...

### Smirnov Trees

2019 Electronic Journal of Combinatorics
We introduce a generalization of Smirnov words in the context of 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.  ...

### Smirnov Trees [article]

2019 arXiv   pre-print
We introduce a generalization of Smirnov words in the context of 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.  ...

### Defining binary phylogenetic trees using parsimony [article]

Mareike Fischer
2021 arXiv   pre-print
It is generally assumed that this criterion works well for data 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.  ...

### Nearly optimal binary search trees

Kurt Mehlhorn
1975 Acta Informatica
Therefore we define the weighted path length of tree T as: Knuth  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.  ...

### Functional Pearls

Jeremy Gibbons
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.  ...

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

Misagh Kordi, Mukul S. Bansal
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.  ...

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

V. Auletta, S.K. Das, A. De Vivo, M.C. Pinotti, V. Scarano
2002 IEEE Transactions on Parallel and Distributed Systems
complete 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.  ...

### Algorithms for Computing Cluster Dissimilarity between Rooted Phylogenetic Trees

Li Shuguang, Liu Zhihui
2015 Open Cybernetics and Systemics Journal
Each vertex of a rooted tree associates 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 .  ...

### 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)
The maximum agreement 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.  ...

### Maximum Covering Subtrees for Phylogenetic Networks [article]

Nathan Davidov, Amanda Hernandez, Justin Jian, Patrick McKenna, K.A. Medlin, Roadra Mojumder, Megan Owen, Andrew Quijano, Amanda Rodriguez, Katherine St. John, Katherine Thai, Meliza Uraga
2020 arXiv   pre-print
Tree-based phylogenetic networks, which may be roughly defined as leaf-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.  ...

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

Paweł Gawrychowski, Jakub Łopuszański
2017 arXiv   pre-print
A 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.  ...   (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.  ...

### TWIX

S. Alireza Aghili, Hua-Gang Li, Divyakant Agrawal, Amr El Abbadi
2006 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.  ...

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

Paweł Gawrychowski, Fabian Kuhn, Jakub Łopuszański, Konstantinos Panagiotou, Pascal Su
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 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  ...

### Efficient Dynamic Embeddings of Binary Trees into Hypercubes

Volker Heun, Ernst W. Mayr
2002 Journal of Algorithms
In this paper, a deterministic algorithm for dynamically embedding 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(  ...
« Previous Showing results 1 — 15 out of 11,863 results