Related papers: Analysis of Smooth Heaps and Slim Heaps

Time-varying mixture densities occur in many scenarios, for example, the distributions of keywords that appear in publications may evolve from year to year, video frame features associated with multiple targets may evolve in a sequence. Any…

This paper describes a new and purely functional implementation technique of binary heaps. A binary heap is a tree-based data structure that implements priority queue operations (insert, remove, minimum/maximum) and guarantees at worst…

Scalable ordered maps must ensure that range queries, which operate over many consecutive keys, provide intuitive semantics (e.g., linearizability) without degrading the performance of concurrent insertions and removals. These goals are…

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 introduce an improved one-shot characterisation of randomness extraction against quantum side information (privacy amplification), strengthening known one-shot bounds and providing a unified derivation of the tightest known asymptotic…

We present several results about position heaps, a relatively new alternative to suffix trees and suffix arrays. First, we show that, if we limit the maximum length of patterns to be sought, then we can also limit the height of the heap and…

Priority queues are data structures that maintain a dynamic collection of elements and allow inserting new elements and removing the smallest element. The most widely known and used priority queue is likely the implicit binary heap, even…

We introduce a new regression problem which we call the Sum-Based Hierarchical Smoothing problem. Given a directed acyclic graph and a non-negative value, called target value, for each vertex in the graph, we wish to find non-negative…

Smoothed analysis is a new way of analyzing algorithms introduced by Spielman and Teng (J. ACM, 2004). Classical methods like worst-case or average-case analysis have accompanying complexity classes, like P and AvgP, respectively. While…

Motivated by the development of computer theory, the sorting algorithm is emerging in an endless stream. Inspired by decrease and conquer method, we propose a brand new sorting algorithmUltimately Heapsort. The algorithm consists of two…

An inherently parallel algorithm is proposed that efficiently performs selection: finding the K-th largest member of a set of N members. Selection is a common component of many more complex algorithms and therefore is a widely studied…

This paper studies the \emph{subset sampling} problem. The input is a set $\mathcal{S}$ of $n$ records together with a function $\textbf{p}$ that assigns each record $v\in\mathcal{S}$ a probability $\textbf{p}(v)$. A query returns a random…

Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…

We present one stable mergesort algorithm, called \Adaptive Shivers Sort, that exploits the existence of monotonic runs for sorting efficiently partially sorted data. We also prove that, although this algorithm is simple to implement, its…

This paper proposes a new concurrent heap algorithm, based on a stateless shape property, which efficiently maintains balance during insert and removeMin operations implemented with hand-over-hand locking. It also provides a O(1)…

We propose an adaptive smoothing algorithm based on Nesterov's smoothing technique in \cite{Nesterov2005c} for solving "fully" nonsmooth composite convex optimization problems. Our method combines both Nesterov's accelerated proximal…

Smoothed analysis is a method for analyzing the performance of algorithms, used especially for those algorithms whose running time in practice is significantly better than what can be proven through worst-case analysis. Spielman and Teng…

Smart Sort algorithm is a "smart" fusion of heap construction procedures (of Heap sort algorithm) into the conventional "Partition" function (of Quick sort algorithm) resulting in a robust version of Quick sort algorithm. We have also…

We study the fully automated amortised analysis of purely functional data structures like skew heaps, as well as weight- and rank-biased leftist heaps. For that we generalise earlier works on automated amortised resource analysis by…

We study the distinct elements and $\ell_p$-heavy hitters problems in the sliding window model, where only the most recent $n$ elements in the data stream form the underlying set. We first introduce the composable histogram, a simple twist…