Related papers: BITS-Tree-An Efficient Data Structure for Segment …

We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it…

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…

A dynamic forest data structure maintains a forest (and associated data like edge weights) under edge insertions and deletions. Dynamic forests are widely used to solve online and offline graph problems. Well-known examples of dynamic…

The dynamic trees problem is to maintain a forest undergoing edge insertions and deletions while supporting queries for information such as connectivity. There are many existing data structures for this problem, but few of them are capable…

We present highly optimized data structures for the dynamic predecessor problem, where the task is to maintain a set $S$ of $w$-bit numbers under insertions, deletions, and predecessor queries (return the largest element in $S$ no larger…

The range-minimum query (RMQ) problem is a fundamental data structuring task with numerous applications. Despite the fact that succinct solutions with worst-case optimal $2n+o(n)$ bits of space and constant query time are known, it has been…

Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…

The performance of today's in-memory indexes is bottlenecked by the memory latency/bandwidth wall. Processing-in-memory (PIM) is an emerging approach that potentially mitigates this bottleneck, by enabling low-latency memory access whose…

The Block Tree (BT) is a novel compact data structure designed to compress sequence collections. It obtains compression ratios close to Lempel-Ziv and supports efficient direct access to any substring. The BT divides the text recursively…

A Concept Tree is a structure for storing knowledge where the trees are stored in a database called a Concept Base. It sits between the highly distributed neural architectures and the distributed information systems, with the intention of…

Indexes are models: a B-Tree-Index can be seen as a model to map a key to the position of a record within a sorted array, a Hash-Index as a model to map a key to a position of a record within an unsorted array, and a BitMap-Index as a model…

Motivation: The comparison of diverse genomic datasets is fundamental to understanding genome biology. Researchers must explore many large datasets of genome intervals (e.g., genes, sequence alignments) to place their experimental results…

Establishing the correspondences between newly acquired points and historically accumulated data (i.e., map) through nearest neighbors search is crucial in numerous robotic applications. However, static tree data structures are inadequate…

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…

We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both…

Database research can help machine learning performance in many ways. One way is to design better data structures. This paper combines the use of incremental computation and sequential and probabilistic filtering to enable "forgetful"…

Index is an important component in database systems. Learned indexes have been shown to outperform traditional tree-based index structures for fixed-sized integer or floating point keys. However, the application of the learned solution to…

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…

Data intensive applications on clusters often require requests quickly be sent to the node managing the desired data. In many applications, one must look through a sorted tree structure to determine the responsible node for accessing or…

In this paper, we revisit the question of how the dynamic optimality of search trees should be defined in external memory. A defining characteristic of external-memory data structures is that there is a stark asymmetry between queries and…