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Binary trees with the largest number of subtrees

L.A. Székely, Hua Wang
2007 Discrete Applied Mathematics  
This paper characterizes binary trees with n leaves, which have the greatest number of subtrees. These binary trees coincide with those which were shown by Fischermann et al.  ...  Math. 122(1-3) (2002) 127-137] and Jelen and Triesch [Superdominance order and distance of trees with bounded maximum degree, Discrete Appl.  ...  Acknowledgment The authors thank Éva Czabarka for her careful reading of an earlier version of the manuscript and useful remarks.  ... 
doi:10.1016/j.dam.2006.05.008 fatcat:awzfgryss5ft5k3om37rv7nbze

On subtrees of trees

L.A. Székely, Hua Wang
2005 Advances in Applied Mathematics  
Wang, Binary trees with the largest number of subtrees, submitted for publication] to binary trees maximizing the total number of subtrees with at least one leaf-this was first investigated by Knudsen  ...  Wang, Binary trees with the largest number of subtrees, submitted for publication], we described the structure of binary trees maximizing the total number of subtrees, here we provide a formula for this  ...  Introduction In [10] we characterized the binary tree on n vertices with the largest number of subtrees.  ... 
doi:10.1016/j.aam.2004.07.002 fatcat:vkv552uj7vfclejhbwkvxeflhe

On the Colijn-Plazzotta numbering scheme for unlabeled binary rooted trees [article]

Noah A Rosenberg
2020 bioRxiv   pre-print
With this ranking, given a number of leaves n, we determine recursions for a_n, the smallest rank assigned to some tree with n leaves, and b_n, the largest rank assigned to some tree with n leaves.  ...  Biol 67:113-126, 2018) introduced a scheme for bijectively associating the unlabeled binary rooted trees with the positive integers. First, the rank 1 is associated with the 1-leaf tree.  ...  Introduction For a given number of leaves n 2, the unlabeled binary rooted trees with n leaves can be obtained recursively (Table 1) .  ... 
doi:10.1101/2020.06.16.155184 fatcat:zl5lf43ryfaljc4n2spyden2ni

Multiset-based Tree Model for Membrane Computing

D. Singh, C.M. Peter
2011 Computer Science Journal of Moldova  
We give formal definitions of a \textit{tree structure} and a \textit{subtree structure} of a tree structure.  ...  We also show that the conventional approach for this representation is not injective from a set of trees to the class of multisets representing such trees.  ...  ACKNOWLEDGEMENT We wish to acknowledge that most of the basic concepts are borrowed from the works of Dershowitz and Manna and that of Gh. Pȃun.  ... 
doaj:9e0280617f764f90ab03f30af1b7a6aa fatcat:gxr7qzo7gvakpdalmjenejve24

Drawing (Complete) Binary Tanglegrams: Hardness, Approximation, Fixed-Parameter Tractability [article]

Kevin Buchin, Maike Buchin, Jaroslaw Byrka, Martin Nöllenburg, Yoshio Okamoto, Rodrigo I. Silveira, Alexander Wolff
2010 arXiv   pre-print
It is known that finding a tanglegram with the minimum number of crossings is NP-hard and that the problem is fixed-parameter tractable with respect to that number.  ...  We show that the maximization version of the dual problem for binary trees can be reduced to a version of MaxCut for which the algorithm of Goemans and Williamson yields a 0.878-approximation.  ...  We thank Danny Holten and Jack van Wijk for introducing us to this exciting problem and David Bryant for pointing us to the work of Roderic Page on host and parasite trees.  ... 
arXiv:0806.0920v3 fatcat:f6dpfahz5vaejfpuwnud6k5nhu

Construction of optimal binary split trees in the presence of bounded access probabilities

J.H Hester, D.S Hirschberg, L.L Larmore
1988 Journal of Algorithms  
A binary split tree is a search structure combining features of heaps and binary search trees.  ...  The fastest known algorithm for building an optimal binary split tree requires (n 4 ) time if the keys are distinct and O(n 5 ) time if the keys are non-distinct.  ...  Huang and Wong 3] de ned generalized binary split trees (GBSTs), which relax the constraint that the key in the root of any subtree be the key with highest access probability of the (remaining) keys in  ... 
doi:10.1016/0196-6774(88)90040-5 fatcat:nb5lofcja5cchk7gcd37tqbv6u

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)  
Given two rooted trees whose leaves are drawn from the same set of items (e.g., species), find the largest subset of these items so that the portions of the two trees restricted to these items are isomorphic  ...  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

A Simple Dynamic Programming Algorithm for Counting Red Nodes in Red-Black Trees

Daxin Zhu, Xiaodong Wang, Jun Tian
2015 International Journal of Future Computer and Communication  
In this paper, we are interested in the number of red nodes in red-black trees.  ...  We first present an O(n 2 log n) time dynamic programming solution for computing r(n), the largest number of red internal nodes in a red-black tree on n keys.  ...  From some examples of the computed red-black trees with largest number of red nodes, we can observe some properties of ) (n r and the corresponding red-black trees as follows. 1) The red-black tree on  ... 
doi:10.7763/ijfcc.2015.v4.357 fatcat:tunpik2wqnbilmi525lk6hsnky

Improved algorithm for maximizing service of carousel storage

Chung-Lun Li, Guohua Wan
2005 Computers & Operations Research  
We consider a problem of maximizing service of a carousel storage system from which items are removed in groups, where each group consists of a certain given number of items of each type.  ...  Kim [4] has developed an algorithm for solving this problem with a running time of O(j 2 ). In this article, we present an algorithm with an improved complexity of O(j log j).  ...  A binary search tree is a binary tree (with no more than two subtrees at each node) having a value associated with each node, such that the value at each node is greater than or equal to any value in the  ... 
doi:10.1016/j.cor.2004.02.005 fatcat:wy5zpmdhmvdehigxnzwb76tdlq

Efficient computation of the iteration of functions

Tsung-Hsi Tsai
2009 Theoretical Computer Science  
Our decompositions minimize the number of recursions in the computation of f m (x) and solve some open problems in Tsaban (Discrete Applied Mathematics 155 (2007) 386-393).  ...  . , N − 1}, we prove that f m (x), the mth iterate of f at x, can be computed in time O(log N) for each natural number m and each x by using O(N) information that is generated in a preprocessing procedure  ...  Acknowledgment We thank the referee for helpful suggestions and comments.  ... 
doi:10.1016/j.tcs.2008.12.019 fatcat:frfbha4lwzdq3p44gkhzoxtsx4

Trees with the most subtrees -- an algorithmic approach [article]

Xiu-Mei Zhang, Xiao-Dong Zhang, Daniel Gray, Hua Wang
2012 arXiv   pre-print
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate  ...  The structures which maximize or minimize the number of subtrees among general trees, binary trees and trees with a given maximum degree have been identified previously.  ...  In the same paper, formulas are given to calculate the number of subtrees of these extremal binary trees.  ... 
arXiv:1210.2871v1 fatcat:jzrucod4lzafxhc44laws4or64

The Common Prefix Problem On Trees [article]

Sreyash Kenkre, Sundar Vishwanathan
2006 arXiv   pre-print
We present a (1-o(1)) factor approximation algorithm for this problem, when the underlying graph is a binary tree.  ...  We then use a result of Feige and Kogan to show that even on stars, the problem is hard to approximate.  ...  We show that binary trees of height log log n also have this property. Claim: The total number of subtrees in a binary tree of height log log n is at most n 2 .  ... 
arXiv:cs/0612060v1 fatcat:xbluzaxoxjagzcs63cvcxuupjm

Faster construction of optimal binary split trees

J.H Hester, D.S Hirschberg, S.-H.S Huang, C.K Wong
1986 Journal of Algorithms  
A binary split tree is a search structure combining features of heaps and binary search trees.  ...  Building an optimal binary split tree was originally conjectured to be intractable due to di culties in applying dynamic programming techniques to the problem.  ...  A simple split value is the value of the largest key in the left subtree.  ... 
doi:10.1016/0196-6774(86)90031-3 fatcat:5eau6csnmnafrmsngjc5oorxwa

Repeated patterns in genetic programming

W. B. Langdon, W. Banzhaf
2007 Natural Computing  
Evolved genetic programming trees contain many repeated code fragments. Size fair crossover limits bloat in automatic programming, preventing the evolution of recurring motifs.  ...  solutions with multiple identical components of different importance.  ...  Source Code A modified version of Andy Singleton's GPquick (GProc) can be obtained via anonymous ftp site cs.ucl.ac.uk directory genetic/gp-code.  ... 
doi:10.1007/s11047-007-9038-8 fatcat:pov2cxnbvfg3biazyc25kqa2mm

Subtree Isomorphism Revisited [article]

Amir Abboud, Arturs Backurs, Thomas Dueholm Hansen, Virginia Vassilevska Williams, Or Zamir
2015 arXiv   pre-print
The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s.  ...  In particular, there is an O({ 2.85^h ,n^2 }) algorithm for binary trees of depth h.  ...  We demonstrate this with a lower bound for the Largest Common Subtree problem, discussed below.  ... 
arXiv:1510.04622v1 fatcat:gnfqh5mcqbaqdavzgs6hsnbm7a
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