English
Related papers

Related papers: De-amortizing Binary Search Trees

200 papers

Binary search trees (BSTs) are one of the most basic and widely used data structures. The best static tree for serving a sequence of queries (searches) can be computed by dynamic programming. In contrast, when the BSTs are allowed to be…

Data Structures and Algorithms · Computer Science 2023-03-07 Yaniv Sadeh , Haim Kaplan

An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost…

Data Structures and Algorithms · Computer Science 2018-06-28 Mordecai Golin , John Iacono , Stefan Langerman , J. Ian Munro , Yakov Nekrich

The tango tree is the first proven $O(\lg \lg n)$-competitive binary search tree (BST). We present the first ever experimental implementation of tango trees and compare the running time of the tango tree with the multi-splay tree and the…

Data Structures and Algorithms · Computer Science 2024-05-30 Khaleel Al-Adhami , Dev Chheda

We present the zipper tree, an $O(\log \log n)$-competitive online binary search tree that performs each access in $O(\log n)$ worst-case time. This shows that for binary search trees, optimal worst-case access time and near-optimal…

Data Structures and Algorithms · Computer Science 2015-05-18 Prosenjit Bose , Karim Douïeb , Vida Dujmovic , Rolf Fagerberg

We consider the problem of computing optimal search trees on trees (STTs). STTs generalize binary search trees (BSTs) in which we search nodes in a path (linear order) to search trees that facilitate search over general tree topologies.…

Data Structures and Algorithms · Computer Science 2025-08-04 Yaniv Sadeh , Haim Kaplan , Uri Zwick

The dynamic set cover problem has been subject to growing research attention in recent years. In this problem, we are given as input a dynamic universe of at most $n$ elements and a fixed collection of $m$ sets, where each element appears…

Data Structures and Algorithms · Computer Science 2024-07-10 Shay Solomon , Amitai Uzrad , Tianyi Zhang

We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is $O(\log^2n)$ bits and it converges in $O(n^2)$ rounds. Thus, this algorithm improves the convergence time of…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-07-26 Lélia Blin , Shlomi Dolev , Maria Potop-Butucaru , Stephane Rovedakis

We present an approach to implement binary search trees in the rule-based graph programming language GP 2. Our implementation uses GP 2's rooted graph transformation rules to be fast and supports insertion, deletion and query operations. We…

Programming Languages · Computer Science 2026-01-08 Ziad Ismaili Alaoui , Detlef Plump

Binary search trees (BST) are a popular type of data structure when dealing with ordered data. Indeed, they enable one to access and modify data efficiently, with their height corresponding to the worst retrieval time. From a probabilistic…

Probability · Mathematics 2025-01-28 Benoît Corsini , Victor Dubach , Valentin Féray

Consider the following generalization of the classic binary search problem: a searcher is required to find a hidden vertex $x$ in a tree $T$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$. After…

Data Structures and Algorithms · Computer Science 2025-10-01 Michał Szyfelbein

We study the dynamic optimality conjecture, which predicts that splay trees are a form of universally efficient binary search tree, for any access sequence. We reduce this claim to a regular access bound, which seems plausible and might be…

Data Structures and Algorithms · Computer Science 2020-04-08 Luís M. S. Russo

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 $O(\log_2n)$…

Data Structures and Algorithms · Computer Science 2018-04-04 Saulo Queiroz

We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each…

Data Structures and Algorithms · Computer Science 2025-05-16 Jingbang Chen , Xinyuan Cao , Alicia Stepin , Li Chen

Adaptive binary search trees are a fundamental data structure for organizing hierarchical information. Their ability to dynamically adjust to access patterns makes them particularly valuable for building responsive and efficient networked…

Data Structures and Algorithms · Computer Science 2025-07-29 Maryam Shiran

A non-blocking chromatic tree is a type of balanced binary search tree where multiple processes can concurrently perform search and update operations. We prove that a certain implementation has amortized cost $O(\dot{c} + \log n)$ for each…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-11-16 Jeremy Ko

At SODA 2009, Demaine et al. presented a novel connection between binary search trees (BSTs) and subsets of points on the plane. This connection was independently discovered by Derryberry et al. As part of their results, Demaine et al.…

Data Structures and Algorithms · Computer Science 2011-05-02 Kyle Fox

This paper proposes a stable sparse rapidly-exploring random trees (SST) algorithm to solve the optimal motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HySST, selects a vertex with the lowest…

Robotics · Computer Science 2023-05-31 Nan Wang , Ricardo G. Sanfelice

We consider a variant of the prize collecting Steiner tree problem in which we are given a \emph{directed graph} $D=(V,A)$, a monotone submodular prize function $p:2^V \rightarrow \mathbb{R}^+ \cup \{0\}$, a cost function $c:V \rightarrow…

Data Structures and Algorithms · Computer Science 2022-10-04 Gianlorenzo D'Angelo , Esmaeil Delfaraz , Hugo Gilbert

Algorithms for efficiently finding optimal alphabetic decision trees -- such as the Hu-Tucker algorithm -- are well established and commonly used. However, such algorithms generally assume that the cost per decision is uniform and thus…

Performance · Computer Science 2007-05-23 Michael B. Baer

Consider the task of performing a sequence of searches in a binary search tree. After each search, we allow an algorithm to arbitrarily restructure the tree. The cost of executing the task is the sum of the time spent searching and the time…

Data Structures and Algorithms · Computer Science 2022-05-10 Caleb C. Levy , Robert E. Tarjan