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This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…

Combinatorics · Mathematics 2026-03-30 Olivier Bodini , Antoine Genitrini , Khaydar Nurligareev

In this paper, we present a distributed algorithm to compute various parameters of a tree such as the process number, the edge search number or the node search number and so the pathwidth. This algorithm requires n steps, an overall…

Discrete Mathematics · Computer Science 2008-12-18 David Coudert , Florian Huc , Dorian Mazauric

We investigate the structural organization of the point-to-point electric, diffusive or hydraulic transport in complex scale-free networks. The random choice of two nodes, a source and a drain, to which a potential difference is applied,…

Local convergence of bounded degree graphs was introduced by Benjamini and Schramm. This result was extended further by Lyons to bounded average degree graphs. In this paper we study the convergence of random tree sequences with given…

Probability · Mathematics 2014-08-07 Attila Deák

The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time…

Populations and Evolution · Quantitative Biology 2008-10-07 David Bryant , Mike Steel

In this work, we are interested in the set of visited vertices of a tree $\mathbb{T}$ by a randomly biased random walk $\mathbb{X}:=(X_n,n \in \mathbb{N})$. The aim is to study a generalized range, that is to say the volume of the trace of…

Probability · Mathematics 2024-09-20 Pierre Andreoletti , Alexis Kagan

Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…

Methodology · Statistics 2025-12-17 Soham Bakshi , Yiling Huang , Snigdha Panigrahi , Walter Dempsey

An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…

Data Structures and Algorithms · Computer Science 2026-02-19 Benjamin Aram Berendsohn

In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning…

Machine Learning · Computer Science 2019-02-14 Erwan Lecarpentier , Guillaume Infantes , Charles Lesire , Emmanuel Rachelson

Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…

Programming Languages · Computer Science 2019-07-03 Reynald Affeldt , Jacques Garrigue , Xuanrui Qi , Kazunari Tanaka

Hybridization networks are representations of evolutionary histories that allow for the inclusion of reticulate events like recombinations, hybridizations, or lateral gene transfers. The recent growth in the number of hybridization network…

Populations and Evolution · Quantitative Biology 2008-07-06 Gabriel Cardona , Merce Llabres , Francesc Rossello , Gabriel Valiente

In recent years, a number of methods have been developed to infer complex demographic histories, especially historical population size changes, from genomic sequence data. Coalescent Hidden Markov Models have proven to be particularly…

Populations and Evolution · Quantitative Biology 2017-10-10 Alexey Miroshnikov , Matthias Steinrücken

Tree-size distribution is one of the most investigated subjects in plant population biology. The forestry literature reports that tree-size distribution trajectories vary across different stands and/or species, while the metabolic scaling…

Populations and Evolution · Quantitative Biology 2012-12-04 Tommaso Anfodillo , Marco Carrer , Filippo Simini , Ionel Popa , Jayanth R. Banavar , Amos Maritan

The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…

Combinatorics · Mathematics 2010-09-27 Omer Angel , Alexander E. Holroyd

We address the problem of summarizing embedded tree patterns extracted from large data trees. We do so by defining and mining closed and maximal embedded unordered tree patterns from a single large data tree. We design an embedded frequent…

Databases · Computer Science 2022-01-11 Xiaoying Wu , Dimitri Theodoratos , Nikos Mamoulis

We comment on old and new results related to the destruction of a random recursive tree (RRT), in which its edges are cut one after the other in a uniform random order. In particular, we study the number of steps needed to isolate or…

Probability · Mathematics 2016-12-28 Erich Baur , Jean Bertoin

In the broadcasting problem on trees, a $\{-1,1\}$-message originating in an unknown node is passed along the tree with a certain error probability $q$. The goal is to estimate the original message without knowing the order in which the…

Probability · Mathematics 2025-09-12 Ernst Althaus , Lisa Hartung , Rebecca Steiner

We study distance properties of a general class of random directed acyclic graphs (DAGs). In a DAG, many natural notions of distance are possible, for there exists multiple paths between pairs of nodes. The distance of interest for circuits…

Probability · Mathematics 2012-11-12 Nicolas Broutin , Omar Fawzi

A tree-packing is a collection of spanning trees of a graph. It has been a useful tool for computing the minimum cut in static, dynamic, and distributed settings. In particular, [Thorup, Comb. 2007] used them to obtain his dynamic min-cut…

Data Structures and Algorithms · Computer Science 2024-12-05 Tijn de Vos , Aleksander B. G. Christiansen

Phylogenetic tree shapes capture fundamental signatures of evolution. We consider ``ranked'' tree shapes, which are equipped with a total order on the internal nodes compatible with the tree graph. Recent work has established an elegant…

Populations and Evolution · Quantitative Biology 2026-03-10 Chris Jennings-Shaffer , Ziyue , Chen , Julia A Palacios , Frederick A Matsen