Related papers: Why some heaps support constant-amortized-time dec…

The pairing heap is a classical heap data structure introduced in 1986 by Fredman, Sedgewick, Sleator, and Tarjan. It is remarkable both for its simplicity and for its excellent performance in practice. The "magic" of pairing heaps lies in…

We present a new threshold phenomenon in data structure lower bounds where slightly reduced update times lead to exploding query times. Consider incremental connectivity, letting t_u be the time to insert an edge and t_q be the query time.…

In the particular case we have insertions/deletions at the tail of a given set S of $n$ one-dimensional elements, we present a simpler and more concrete algorithm than that presented in [Anderson, 2007] achieving the same (but also…

We analyze union-find using potential functions motivated by continuous algorithms, and give alternate proofs of the $O(\log\log{n})$, $O(\log^{*}n)$, $O(\log^{**}n)$, and $O(\alpha(n))$ amortized cost upper bounds. The proof of the…

Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…

The list-labeling problem captures the basic task of storing a dynamically changing set of up to $n$ elements in sorted order in an array of size $m = (1 + \Theta(1))n$. The goal is to support insertions and deletions while moving around…

The online list labeling problem is an algorithmic primitive with a large literature of upper bounds, lower bounds, and applications. The goal is to store a dynamically-changing set of $n$ items in an array of $m$ slots, while maintaining…

We seek to perform efficient queries for the predecessor among $n$ values stored in $k$ sorted arrays. Evading the $\Omega(n \log k)$ lower bound from merging $k$ arrays, we support predecessor queries in $O(\log n)$ time after $O(n…

Chazelle [JACM00] introduced the soft heap as a building block for efficient minimum spanning tree algorithms, and recently Kaplan et al. [SOSA2019] showed how soft heaps can be applied to achieve simpler algorithms for various selection…

For nearly six decades, the central open question in the study of hash tables has been to determine the optimal achievable tradeoff curve between time and space. State-of-the-art hash tables offer the following guarantee: If keys/values are…

We analyze priority queues of Fibonacci family. The paper is inspired by Violation heap [1], where A. Elmasry saves one pointer in representation of Fibonacci heap nodes while achieving the same amortized bounds as Fibonacci heaps [2] of M.…

This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose…

Linear-probing hash tables have been classically believed to support insertions in time $\Theta(x^2)$, where $1 - 1/x$ is the load factor of the hash table. Recent work by Bender, Kuszmaul, and Kuszmaul (FOCS'21), however, has added a new…

The suffix array and the suffix tree are the two most fundamental data structures for string processing. For a length-$n$ text, however, they use $\Theta(n \log n)$ bits of space, which is often too costly. To address this, Grossi and…

Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…

Given a set $ P $ of $n$ points and a set $ H $ of $n$ half-planes in the plane, we consider the problem of computing a smallest subset of points such that each half-plane contains at least one point of the subset. The previously best…

Leftist heaps and skew heaps are two well-known data structures for mergeable priority queues. Leftist heaps are constructed for efficiency in the worst-case sense whereas skew heaps are self-adjusting, designed for efficiency in the…

Price-based revenue management is an important problem in operations management with many practical applications. The problem considers a retailer who sells a product (or multiple products) over $T$ consecutive time periods and is subject…

A priority queue is a fundamental data structure that maintains a dynamic set of (key, priority)-pairs and supports Insert, Delete, ExtractMin and DecreaseKey operations. In the external memory model, the current best priority queue…

This article introduces a new optimization method to improve mergesort's runtime complexity, when sorting sequences that have equal keys to $O(n log_2 k)$, where $k$ is the number of distinct keys in the sequence. When $k$ is constant, it…