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We describe a framework for maintaining forest algebra representations that are of logarithmic height for unranked trees. Such representations can be computed in O(n) time and updated in O(log(n)) time. The framework is of potential…

Logic in Computer Science · Computer Science 2025-10-08 Sarah Kleest-Meißner , Jonas Marasus , Matthias Niewerth

In many applications, e.g., recommender systems and traffic monitoring, the data comes in the form of a matrix that is only partially observed and low rank. A fundamental data-analysis task for these datasets is matrix completion, where the…

Machine Learning · Computer Science 2017-05-02 Natali Ruchansky , Mark Crovella , Evimaria Terzi

Augmenting an existing sequential data structure with extra information to support greater functionality is a widely used technique. For example, search trees are augmented to build sequential data structures like order-statistic trees,…

Data Structures and Algorithms · Computer Science 2024-05-20 Panagiota Fatourou , Eric Ruppert

In this paper we propose a dynamic data structure that supports efficient algorithms for updating and querying singly connected Bayesian networks (causal trees and polytrees). In the conventional algorithms, new evidence in absorbed in time…

Artificial Intelligence · Computer Science 2014-08-08 Arthur L. Delcher , Adam J. Grove , Simon Kasif , Judea Pearl

$k$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,…

Data Structures and Algorithms · Computer Science 2021-12-14 Rahul Yesantharao , Yiqiu Wang , Laxman Dhulipala , Julian Shun

We study dynamic algorithms for maintaining fundamental algebraic properties of matrices, specifically, rank, basis, and full-rank submatrices, with applications to maximum matching on dynamic graphs. Prior dynamic algorithms for rank…

Data Structures and Algorithms · Computer Science 2026-05-12 Jan van den Brand , Vishal Kumar , Daniel J. Zhang

We show how a few modifications to the red-black trees allow for $O(1)$ worst-case update time (once the position of the inserted or deleted element is known). The resulting structure is based on relaxing some of the properties of the…

Data Structures and Algorithms · Computer Science 2018-04-09 Amr Elmasry , Mostafa Kahla , Fady Ahdy , Mahmoud Hashem

We suggest a new non-recursive algorithm for constructing a binary search tree given an array of numbers. The algorithm has $O(N)$ time and $O(1)$ memory complexity if the given array of $N$ numbers is sorted. The resulting tree is of…

Data Structures and Algorithms · Computer Science 2022-07-20 Pavel S. Ruzankin

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…

Data Structures and Algorithms · Computer Science 2021-05-31 Piotr Borowiecki , Dariusz Dereniowski , Dorota Osula

The M-tree is a paged, dynamically balanced metric access method that responds gracefully to the insertion of new objects. To date, no algorithm has been published for the corresponding Delete operation. We believe this to be non-trivial…

Databases · Computer Science 2010-04-27 Alan P. Sexton , Richard Swinbank

Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently,…

Data Structures and Algorithms · Computer Science 2017-05-11 Shahbaz Khan

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…

Data Structures and Algorithms · Computer Science 2024-03-08 Brent Harrison , Jason Necaise , Andrew Projansky , James D. Whitfield

We study subgraph counting over fully dynamic graphs, which undergo edge insertions and deletions. Counting subgraphs is a fundamental problem in graph theory with numerous applications across various fields, including database theory,…

Data Structures and Algorithms · Computer Science 2025-04-16 Sepehr Assadi , Vihan Shah

We present a data structure that in a dynamic graph of treedepth at most $d$, which is modified over time by edge insertions and deletions, maintains an optimum-height elimination forest. The data structure achieves worst-case update time…

Building concurrent spatial trees is more complicated than binary search trees since a space hierarchy should be preserved during modifications. We present a non-blocking quadtree-quadboost-that supports concurrent insert, remove, move, and…

Data Structures and Algorithms · Computer Science 2016-07-13 Keren Zhou , Guangming Tan , Wei Zhou

Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst-case guarantees. We propose a new data…

Data Structures and Algorithms · Computer Science 2022-07-19 Qing Chen , Oded Lachish , Sven Helmer , Michael Böhlen

In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…

Data Structures and Algorithms · Computer Science 2016-05-09 Daniel Shea

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…

Databases · Computer Science 2023-10-10 Ilya Kokorin , Dan Alistarh , Vitaly Aksenov

Spanning trees of low average stretch on the non-tree edges, as introduced by Alon et al. [SICOMP 1995], are a natural graph-theoretic object. In recent years, they have found significant applications in solvers for symmetric diagonally…

Data Structures and Algorithms · Computer Science 2019-08-01 Sebastian Forster , Gramoz Goranci

Augmented B-trees (aB-trees) are a broad class of data structures. The seminal work "succincter" by Patrascu showed that any aB-tree can be stored using only two bits of redundancy, while supporting queries to the tree in time proportional…

Data Structures and Algorithms · Computer Science 2023-09-25 Tianxiao Li , Jingxun Liang , Huacheng Yu , Renfei Zhou