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Binary trees with the largest number of subtrees

2007
*
Discrete Applied Mathematics
*

This paper characterizes

doi:10.1016/j.dam.2006.05.008
fatcat:awzfgryss5ft5k3om37rv7nbze
*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. ...##
###
On subtrees of trees

2005
*
Advances in Applied Mathematics
*

Wang,

doi:10.1016/j.aam.2004.07.002
fatcat:vkv552uj7vfclejhbwkvxeflhe
*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*. ...##
###
On the Colijn-Plazzotta numbering scheme for unlabeled binary rooted trees
[article]

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) . ...

##
###
Multiset-based Tree Model for Membrane Computing

2011
*
Computer Science Journal of Moldova
*

We give formal definitions

doaj:9e0280617f764f90ab03f30af1b7a6aa
fatcat:gxr7qzo7gvakpdalmjenejve24
*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. ...##
###
Drawing (Complete) Binary Tanglegrams: Hardness, Approximation, Fixed-Parameter Tractability
[article]

2010
*
arXiv
*
pre-print

It is known that finding a tanglegram

arXiv:0806.0920v3
fatcat:f6dpfahz5vaejfpuwnud6k5nhu
*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*. ...##
###
Construction of optimal binary split trees in the presence of bounded access probabilities

1988
*
Journal of Algorithms
*

A

doi:10.1016/0196-6774(88)90040-5
fatcat:nb5lofcja5cchk7gcd37tqbv6u
*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 ...##
###
An O(nlog n) Algorithm for the Maximum Agreement Subtree Problem for Binary Trees

2000
*
SIAM journal on computing (Print)
*

Given two rooted

doi:10.1137/s0097539796313477
fatcat:b4undpqm3jfj7nvfqmmlvkmwkq
*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. ...##
###
A Simple Dynamic Programming Algorithm for Counting Red Nodes in Red-Black Trees

2015
*
International Journal of Future Computer and Communication
*

In this paper, we are interested in

doi:10.7763/ijfcc.2015.v4.357
fatcat:tunpik2wqnbilmi525lk6hsnky
*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 ...##
###
Improved algorithm for maximizing service of carousel storage

2005
*
Computers & Operations Research
*

We consider a problem

doi:10.1016/j.cor.2004.02.005
fatcat:wy5zpmdhmvdehigxnzwb76tdlq
*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*...##
###
Efficient computation of the iteration of functions

2009
*
Theoretical Computer Science
*

Our decompositions minimize

doi:10.1016/j.tcs.2008.12.019
fatcat:frfbha4lwzdq3p44gkhzoxtsx4
*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. ...##
###
Trees with the most subtrees -- an algorithmic approach
[article]

2012
*
arXiv
*
pre-print

When considering

arXiv:1210.2871v1
fatcat:jzrucod4lzafxhc44laws4or64
*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*. ...##
###
The Common Prefix Problem On Trees
[article]

2006
*
arXiv
*
pre-print

We present a (1-o(1)) factor approximation algorithm for this problem, when

arXiv:cs/0612060v1
fatcat:xbluzaxoxjagzcs63cvcxuupjm
*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 . ...##
###
Faster construction of optimal binary split trees

1986
*
Journal of Algorithms
*

A

doi:10.1016/0196-6774(86)90031-3
fatcat:5eau6csnmnafrmsngjc5oorxwa
*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*. ...##
###
Repeated patterns in genetic programming

2007
*
Natural Computing
*

Evolved genetic programming

doi:10.1007/s11047-007-9038-8
fatcat:pov2cxnbvfg3biazyc25kqa2mm
*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. ...##
###
Subtree Isomorphism Revisited
[article]

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. ...

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