Related papers: Binary Join Trees
Binary Partition Hierarchies (BPH) and minimum spanning trees are fundamental data structures involved in hierarchical analysis such as quasi-flat zones or watershed. However, classical BPH construction algorithms require to have the whole…
This paper describes a new and purely functional implementation technique of binary heaps. A binary heap is a tree-based data structure that implements priority queue operations (insert, remove, minimum/maximum) and guarantees at worst…
We develop a purely set-theoretic formalism for binary trees and binary graphs. We define a category of binary automata, and display it as a fibred category over the category of binary graphs. We also relate the notion of binary graphs to…
The junction tree algorithm is a way of computing marginals of boolean multivariate probability distributions that factorise over sets of random variables. The junction tree algorithm first constructs a tree called a junction tree who's…
The efficiency of inference in both the Hugin and, most notably, the Shafer-Shenoy architectures can be improved by exploiting the independence relations induced by the incoming messages of a clique. That is, the message to be sent from a…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
Decision systems deal with a large volume of data stored in new databases called data warehouses. Data warehouses are typically modeled by a star schema that conventionally presents a central fact table and a set of dimension tables. The…
A decision tree looks like a simple directed acyclic computational graph, where only the leaf nodes specify the output values and the non-terminals specify their tests or split conditions. From the numerical perspective, we express decision…
Work introduces a hierarchical binary tree-based reduction that replaces standard self-attention. The core idea is to use a recursive Gated Linear Unit merge operation, achieving O(n) total merge operations O(log n) parallel depth O(n d^2)…
We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all them when seen as isomorphic with the set of…
We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank…
The binary indexed tree, or Fenwick tree, is a data structure that can efficiently update values and calculate prefix sums in an array. It allows both of these operations to be performed in $O(\log_2 N)$ time. Here we present a novel data…
Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
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…
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…
Various real-life applications, for example, Internet of Things, wireless sensor networks, smart grids, transportation networks, communication networks, social networks, and computer grid systems, are always modeled as network structures.…
In this paper we consider the enumeration of binary trees avoiding non-contiguous binary tree patterns. We begin by computing closed formulas for the number of trees avoiding a single binary tree pattern with 4 or fewer leaves and compare…
When considering 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 to other graphical indices in…
The Binary Search Tree (BST) is average in computer science which supports a compact data structure in memory and oneself even conducts a row of quick algorithms, by which people often apply it in dynamical circumstance. Besides these…