Related papers: Zip Trees
We examine a discrete random recursive tree growth process that, at each time step, either adds or deletes a node from the tree with probability $p$ and $1-p$, respectively. Node addition follows the usual uniform attachment model. For node…
We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by…
We present an axiomatic framework for analyzing the algorithmic properties of decision trees. This framework supports the classification of decision tree problems through structural and ancestral constraints within a rigorous mathematical…
Given a text, rank and select queries return the number of occurrences of a character up to a position (rank) or the position of a character with a given rank (select). These queries have applications in, e.g., compression, computational…
We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…
We study the dynamic optimality conjecture, which predicts that splay trees are a form of universally efficient binary search tree, for any access sequence. We reduce this claim to a regular access bound, which seems plausible and might be…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
The tree-depth problem can be seen as finding an elimination tree of minimum height for a given input graph $G$. We introduce a bicriteria generalization in which additionally the width of the elimination tree needs to be bounded by some…
Decision trees are among the most popular machine learning models and are used routinely in applications ranging from revenue management and medicine to bioinformatics. In this paper, we consider the problem of learning optimal binary…
The heap is a basic data structure used in a wide variety of applications, including shortest path and minimum spanning tree algorithms. In this paper we explore the design space of comparison-based, amortized-efficient heap…
An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…
We investigate the distribution of the depth of a node containing a specific key or, equivalently, the number of steps needed to retrieve an item stored in a randomly grown binary search tree. Using a representation in terms of mixed and…
Decision trees are powerful tools for classification and regression that attract many researchers working in the burgeoning area of machine learning. One advantage of decision trees over other methods is their interpretability, which is…
A uniform attachment tree is a random tree that is generated dynamically. Starting from a fixed "seed" tree, vertices are added sequentially by attaching each vertex to an existing vertex chosen uniformly at random. Upon observing a large…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…
Random Forests have been one of the most popular bagging methods in the past few decades, especially due to their success at handling tabular datasets. They have been extensively studied and compared to boosting models, like XGBoost, which…
Decision trees remain one of the most popular machine learning models today, largely due to their out-of-the-box performance and interpretability. In this work, we present a Bayesian approach to decision tree induction via maximum a…
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…
A uniform recursive tree on $n$ vertices is a random tree where each possible $(n-1)!$ labeled recursive rooted tree is selected with equal probability. In this paper we introduce and study weighted trees, a non-uniform recursive tree model…