Related papers: Partition-based Simple Heaps
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…
We study the point location problem in incremental (possibly disconnected) planar subdivisions, that is, dynamic subdivisions allowing insertions of edges and vertices only. Specifically, we present an $O(n\log n)$-space data structure for…
A lattice is a partially-ordered set in which every pair of elements has a unique meet (greatest lower bound) and join (least upper bound). We present new data structures for lattices that are simple, efficient, and nearly optimal in terms…
We consider the problem of sorting $n$ items, given the outcomes of $m$ pre-existing comparisons. We present a simple and natural deterministic algorithm that runs in $O(m + \log T)$ time and does $O(\log T)$ comparisons, where $T$ is the…
This paper presents a comprehensive overview of monotone priority queues, focusing on their evolution and application in shortest path algorithms. Monotone priority queues are characterized by the property that their minimum key does not…
This paper describes a heap construction that supports insert and delete operations in arbitrary (possibly illegitimate) states. After any sequence of at most O(m) heap operations, the heap state is guarantee to be legitimate, where m is…
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…
The layer-ordered heap (LOH) is a simple, recently proposed data structure used in optimal selection on $X+Y$, thealgorithm with the best known runtime for selection on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for computing…
In many applications of clustering (for example, ontologies or clusterings of animal or plant species), hierarchical clusterings are more descriptive than a flat clustering. A hierarchical clustering over $n$ elements is represented by a…
This note makes an observation that significantly simplifies a number of previous parallel, two-way merge algorithms based on binary search and sequential merge in parallel. First, it is shown that the additional merge step of distinguished…
We study robust and efficient distributed algorithms for building and maintaining distributed data structures in dynamic Peer-to-Peer (P2P) networks. P2P networks are characterized by a high level of dynamicity with abrupt heavy node…
Let $S \subseteq \mathbb{R}^2$ be a set of $n$ \emph{sites} in the plane, so that every site $s \in S$ has an \emph{associated radius} $r_s > 0$. Let $D(S)$ be the \emph{disk intersection graph} defined by $S$, i.e., the graph with vertex…
Priority queues with parallel access are an attractive data structure for applications like prioritized online scheduling, discrete event simulation, or greedy algorithms. However, a classical priority queue constitutes a severe bottleneck…
The "ordered set" abstract data type with operations "insert", "erase", "find", "min", "max", "next" and "prev" is ubiquitous in computer science. It is usually implemented with red-black trees, $B$-trees, or $B^+$-trees. We present our…
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
Skip graphs are a novel distributed data structure, based on skip lists, that provide the full functionality of a balanced tree in a distributed system where resources are stored in separate nodes that may fail at any time. They are…
We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures. Roughly speaking, we map an arbitrary heap algorithm within…
Learned indexes leverage machine learning models to accelerate query answering in databases, showing impressive practical performance. However, theoretical understanding of these methods remains incomplete. Existing research suggests that…
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…
We develop dynamic data structures for maintaining a hierarchical k-center clustering when the points come from a discrete space $\{1,\ldots,\Delta\}^d$. Our first data structure is for the low dimensional setting, i.e., d is a constant,…