A linear time complexity of breadth-first search using P system with membrane division by Salehi, Einallah, Shamsuddin, Siti Mariyam, Nemati, Kourosh

“…The theorem shows time complexity of BSF in this framework on randomly binary trees reduced from O (2 d) to O (d)…”
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Constructing phylogenetic networks via cherry picking and machine learning by Giulia Bernardini, Leo van Iersel, Esther Julien, Leen Stougie

“…Results In this paper, we apply the recently-introduced theoretical framework of cherry picking to design a class of efficient heuristics that are guaranteed to produce a network containing each of the input trees, for practical-size datasets consisting of binary trees. Some of the heuristics in this framework are based on the design and training of a machine learning model that captures essential information on the structure of the input trees and guides the algorithms towards better solutions. …”
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Pattern avoidance for alternating permutations and reading words of tableaux by Lewis, Joel Brewster

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Structural Patterns in Complex Systems Using Multidendrograms by Sergio Gómez, Alberto Fernández, Clara Granell, Alex Arenas

“…This problem arises when there are more than two clusters separated by the same maximum similarity (or minimum distance) during the agglomerative process. Forcing binary trees in this case means breaking ties in some way, thus giving rise to different output clusterings depending on the criterion used. …”
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I-theory on depth vs width: hierarchical function composition by Poggio, Tomaso, Anselmi, Fabio, Rosasco, Lorenzo

“…Deep learning networks with convolution, pooling and subsampling are a special case of hierar- chical architectures, which can be represented by trees (such as binary trees). Hierarchical as well as shallow networks can approximate functions of several variables, in particular those that are com- positions of low dimensional functions. …”
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Improved parallel construction of wavelet trees and rank/select structures by Shun, Julian

“…We then show how to use similar ideas to construct variants of wavelet trees (arbitrary-shaped binary trees and multiary trees) as well as wavelet matrices in parallel with lower work complexity than prior algorithms. …”
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Brain-wide dendrites in a near-optimal performance of dynamic range and information transmission by Congping Lin, Fan Xu, Yiwei Zhang

“…We model dendrites in a neuron as multiple excitable binary trees connected to the soma where each node in a tree can be excited by external stimulus or by receiving signals transmitted from adjacent excited nodes. …”
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Look-Ahead Strategies in One Person Games with Randomly Generated Game Trees by Johnson, David S.

“…A random method for generated binary trees is presented, ad twp forms of a class of one person games called, "Tree Solitaire" which have such trees as their game trees are defined. …”
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Extensions for Apple-Google exposure notification mechanism by Adam Bobowski, Jacek Cichoń, Mirosław Kutyłowski

“…We have detected some unexpected phenomena regarding the number of keys for unbalanced binary trees of a small size. These observations may be used in case that the size of the lists of diagnosis keys has to be optimized.…”
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Counting Markov equivalence classes for DAG models on trees by Radhakrishnan, Adityanarayanan, Solus, Liam, Uhler, Caroline

“…We describe these polynomials for some well-studied families of graphs including paths, stars, cycles, spider graphs, caterpillars, and balanced binary trees. In doing so, we recover connections to independence polynomials, and extend some classical identities that hold for Fibonacci numbers. …”
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Limiting behaviour of combinatorial Markov chains by Soerensen, F

“…Firstly, in the special case of γ = 1 − α, the stable tree growth process, we generalize a Markov chain by Aldous on binary trees, and show that an unrooted version of the chain has relaxation time of exactly order n² , whilst the relaxation time for a rooted version is at least of order n² and at most of order n^3−α . …”

AQMDRL: Automatic Quality of Service Architecture Based on Multistep Deep Reinforcement Learning in Software-Defined Networking by Junyan Chen, Cenhuishan Liao, Yong Wang, Lei Jin, Xiaoye Lu, Xiaolan Xie, Rui Yao

“…In addition, we adapt a prioritized experience sampling based on SumTree binary trees to improve the convergence rate of the multistep DDPG algorithm. …”
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Machine Learning Prediction of Hypoglycemia and Hyperglycemia From Electronic Health Records: Algorithm Development and Validation by Harald Witte, Christos Nakas, Lia Bally, Alexander Benedikt Leichtle

“…Using patient details and routine data from electronic health records, a multiclass prediction model for BG decompensation events (<3.9 mmol/L [hypoglycemia] or >10, >13.9, or >16.7 mmol/L [representing different degrees of hyperglycemia]) was generated based on a second-level ensemble of gradient-boosted binary trees. ResultsA total of 63,579 hospital admissions of 38,250 patients were included in this study. …”
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Counting Markov equivalence classes for DAG models on trees by Radhakrishnan, Adityanarayanan, Solus, Liam, Uhler, Caroline

“…We describe these polynomials for some well-studied families of graphs including paths, stars, cycles, spider graphs, caterpillars, and balanced binary trees. In doing so, we recover connections to independence polynomials, and extend some classical identities that hold for Fibonacci numbers. …”
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Subtree Isomorphism Revisited by Abboud, Amir, Backurs, Arturs, Hansen, Thomas Dueholm, Vassilevska Williams, Virginia, Zamir, Or

“…In particular, there is an O(min{2.85h,n2}) algorithm for binary trees of depth h. Our reductions utilize new “tree gadgets” that are likely useful for future SETH-based lower bounds for problems on trees. …”
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On coalescence time in graphs–when is coalescing as fast as meeting? by Kanade, V, Mallmann-Trenn, F, Sauerwald, T

“…Despite recent progress such as by Cooper et&nbsp;al. [14] and Cooper et&nbsp;al. [19], the coalescence time for graphs such as binary trees,&nbsp;<em>d</em>-dimensional tori, hypercubes and more generally, vertex-transitive graphs, remains unresolved.…”

Complexity issues in general purpose parallel computing by Chin, D, Chin, Douglas Andrew

“…</p> <p>In the thesis we present Block PRAM algorithms and lower bounds for specific problems on arrays, lists, expression trees, graphs, strings, binary trees and butterflies. These results introduce useful basic techniques for parallel computation in practice, and provide a classification of problems and algorithms according to their granularity. …”

On the Communication Complexity of Read-Once AC^0 Formulae by Kopparty, Swastik, Raghavendra, Prasad, Jayram, T. S

“…Our analysis for trees of depth d proceeds in two steps: (1) reduction to measuring the information complexity of binary depth-d trees, and (2) proving lower bounds on the information complexity of binary trees. In order to execute this program, we carefully construct input distributions under which both these steps can be carried out simultaneously. …”
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Efficient classical simulation of spin networks by Sylvester, Igor Andrade

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On coalescence time in graphs: When is coalescing as fast as meeting? by Kanade, V, Sauerwald, T, Mallmann-Trenn, F

“…Despite recent progress such as by Cooper, Elsasser, Ono, Radzik [13] and Cooper, Frieze and Radzik [12], the coalescence time for graphs such as binary trees, d-dimensional tori, hypercubes and more generally, vertex-transitive graphs, remains unresolved.…”