Related papers: A Dynamic, Self-balancing k-d Tree

Recent theory work has found that a special type of spatial partition tree - called a random projection tree - is adaptive to the intrinsic dimension of the data from which it is built. Here we examine this same question, with a combination…

Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…

In this work, we propose D3-Tree, a dynamic distributed deterministic structure for data management in decentralized networks. We present in brief the theoretical algorithmic analysis, in which our proposed structure is based on, and we…

In this paper, we revisit the problem of indexing multi-dimensional data in memory for the efficient support of multi-dimensional range queries and nearest neighbor queries. This is a classic problem in main-memory databases, where there is…

Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…

The paper presents a technique for constructing noisy data structures called a walking tree. We apply it for a Red-Black tree (an implementation of a Self-Balanced Binary Search Tree) and a segment tree. We obtain the same complexity of the…

We present a new overlay, called the {\em Deterministic Decentralized tree} ($D^2$-tree). The $D^2$-tree compares favourably to other overlays for the following reasons: (a) it provides matching and better complexities, which are…

We introduce dynamic smooth (a.k.a. balanced) compressed quadtrees with worst-case constant time updates in constant dimensions. We distinguish two versions of the problem. First, we show that quadtrees as a space-division data structure…

The k-d tree is a classic binary space-partitioning tree used to organize points in k-dimensional space. While used in computational geometry and graphics, the data structure has a long history of application in nearest neighbor search. The…

$k$d-trees are widely used in parallel databases to support efficient neighborhood/similarity queries. Supporting parallel updates to $k$d-trees is therefore an important operation. In this paper, we present BDL-tree, a parallel,…

We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…

This paper presents a new kind of self-balancing ternary search trie that uses a randomized balancing strategy adapted from Aragon and Seidel's randomized binary search trees ("treaps"). After any sequence of insertions and deletions of…

A buffer k-d tree is a k-d tree variant for massively-parallel nearest neighbor search. While providing valuable speed-ups on modern many-core devices in case both a large number of reference and query points are given, buffer k-d trees are…

Data augmentation is widely used for training a neural network given little labeled data. A common practice of augmentation training is applying a composition of multiple transformations sequentially to the data. Existing augmentation…

Since AVL trees were invented in 1962, two major open questions about rebalancing operations, which found positive answers in other balanced binary search trees, were left open: can these operations be performed top-down (with a fixed…

Manipulating downward-closed sets of vectors forms the basis of so-called antichain-based algorithms in verification. In that context, the dimension of the vectors is intimately tied to the size of the input structure to be verified. In…

Tree data structures, such as red-black trees, quad trees, treaps, or tries, are fundamental tools in computer science. A classical problem in concurrency is to obtain expressive, efficient, and scalable versions of practical tree data…

The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…

The computation of feedback control using Dynamic Programming equation is a difficult task due the curse of dimensionality. The tree structure algorithm is one the methods introduced recently that mitigate this problem. The method computes…

Tree embedding has been a fundamental method in algorithm design with wide applications. We focus on the efficiency of building tree embedding in various computational settings under high-dimensional Euclidean $\mathbb{R}^d$. We devise a…