Related papers: Radix sort trees in the large

We extend the left-to-right Lyndon factorisation of a word to the left Lyndon tree construction of a Lyndon word. It yields an algorithm to sort the prefixes of a Lyndon word according to the infinite ordering defined by Dolce et al.…

This dissertation focuses on two fundamental sorting problems: string sorting and suffix sorting. The first part considers parallel string sorting on shared-memory multi-core machines, the second part external memory suffix sorting using…

Given two messages - as linear sequences of letters, it is immediate to determine whether one can be transformed into the other by simple substitution cipher of the letters. On the other hand, if the letters are carried as labels on nodes…

We prove that a uniform, rooted unordered binary tree with $n$ vertices has the Brownian continuum random tree as its scaling limit for the Gromov-Hausdorff topology. The limit is thus, up to a constant factor, the same as that of uniform…

We study Bernoulli bond percolation on a random recursive tree of size $n$ with percolation parameter $p(n)$ converging to $1$ as $n$ tends to infinity. The sizes of the percolation clusters are naturally stored in a tree. We prove…

We address the problem of ordering trees with the same degree sequence by their spectral radii. To achieve that, we consider 2-switch transformations which preserve the degree sequence and establish when the index decreases. Our main…

We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…

We study the growth of a time-ordered rooted tree by probabilistic attachment of new vertices to leaves. We construct a likelihood function of the leaves based on the connectivity of the tree. We take such connectivity to be induced by the…

We investigate the structural relationship between prefix-free codes over the binary alphabet and a class of unlabeled rooted trees, which we call \emph{symmetric} trees. We establish a canonical correspondence between prefix-free codes and…

Binary search trees (BST) are a popular type of data structure when dealing with ordered data. Indeed, they enable one to access and modify data efficiently, with their height corresponding to the worst retrieval time. From a probabilistic…

A $B$-tree is a type of search tree where every node (except possibly for the root) contains between $m$ and $2m$ keys for some positive integer $m$, and all leaves have the same distance to the root. We study sequences of $B$-trees that…

We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…

Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…

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…

We address the problem of learning binary decision trees that partition data for some downstream task. We propose to learn discrete parameters (i.e., for tree traversals and node pruning) and continuous parameters (i.e., for tree split…

Let T d (n) be the set of d-ary rooted trees with n internal nodes. We give a method to construct a sequence (t n , n $\ge$ 0) where, for any n $\ge$ 1, t n has the uniform distribution in T d (n), and t n is constructed from t n--1 by the…

Efficiently word storing and searching is an important task in computer science. An application space complexity, time complexity, and overall performance depend on this string data. Many word searching data structures and algorithms exist…

An m-extracting procedure produces unbiased random bits from a loaded dice with m faces. A binarization takes inputs from an m-faced dice and produce bit sequences to be fed into a (binary) extracting procedure to obtain random bits. Thus,…

A trie $\mathcal{T}$ is a rooted tree such that each edge is labeled by a single character from the alphabet, and the labels of out-going edges from the same node are mutually distinct. Given a trie $\mathcal{T}$ with $n$ edges, we show how…

A central limit theorem for binary tree is numerically examined. Two types of central limit theorem for higher-order branches are formulated. A topological structure of a binary tree is expressed by a binary sequence, and the…