Related papers: A Dynamic, Self-balancing k-d Tree
Distributed databases often suffer unequal distribution of data among storage nodes, which is known as `data skew'. Data skew arises from a number of causes such as removal of existing storage nodes and addition of new empty nodes to the…
This paper studies the empirical behaviour of the p-AVL tree, a probabilistic variant of the AVL tree in which each imbalance is repaired with probability $p$. This gives an exact continuous interpolation from $p = 0$, which recovers the…
We consider the K-satisfiability problem on a regular d-ary rooted tree. For this model, we demonstrate how we can calculate in closed form, the moments of the total number of solutions as a function of d and K, where the average is over…
Datacenter networks are becoming increasingly flexible with the incorporation of new networking technologies, such as optical circuit switches. These technologies allow for programmable network topologies that can be reconfigured to better…
We study the integration of machine learning advice to improve upon traditional data structure designed for efficient search queries. Although there has been recent effort in improving the performance of binary search trees using machine…
A central challenge in scaling up explicit state-space search for large tasks is compactly representing the set of generated states. Tree databases, a data structure from model checking, require constant space per generated state in the…
We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…
In particle simulations, the weights of particles determine how many physical particles they represent. Adaptively adjusting these weights can greatly improve the efficiency of the simulation, without creating severe nonphysical artifacts.…
While the algorithmic drawing of static trees is well-understood and well-supported by software tools, creating animations depicting how a tree changes over time is currently difficult: software support, if available at all, is not…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field…
The basic idea of the kd-tree algorithm is to recursively partition a point set P by hyperplanes, and to store the obtained partitioning in a binary tree. Due to its immense popularity, many applications in astronomy have been implemented.…
We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to…
The history of gene families -- which are equivalent to event-labeled gene trees -- can to some extent be reconstructed from empirically estimated evolutionary event-relations containing pairs of orthologous, paralogous or xenologous genes.…
Although deep learning models owe their remarkable success to deep and complex architectures, this very complexity typically comes at the expense of real-time performance. To address this issue, a variety of model compression techniques…
In this paper, we present fixed-parameter tractability algorithms for both the undirected and directed versions of the Spanning Tree Isomorphism Problem, parameterized by the size $k$ of a redundant set. A redundant set is a collection of…
In this paper, we introduce a collaborative training algorithm of balanced random forests with convolutional neural networks for domain adaptation tasks. In real scenarios, most domain adaptation algorithms face the challenges from noisy,…
The k-d tree was one of the first spatial data structures proposed for nearest neighbor search. Its efficacy is diminished in high-dimensional spaces, but several variants, with randomization and overlapping cells, have proved to be…
Ordered sequences of data, specified with a join operation to combine sequences, serve as a foundation for the implementation of parallel functional algorithms. This abstract data type can be elegantly and efficiently implemented using…
A simple and computationally efficient scheme for tree-structured vector quantization is presented. Unlike previous methods, its quantization error depends only on the intrinsic dimension of the data distribution, rather than the apparent…
In this paper we generalize the definition of "Search Trees" (ST) to enable reference values other than the key of prior inserted nodes. The idea builds on the assumption an $n$-node AVL (or Red-Black) requires to assure $O(\log_2n)$…