Related papers: The Quicksort Process
Algorithms which sort lists of real numbers into ascending order have been studied for decades. They are typically based on a series of pairwise comparisons and run entirely on chip. However people routinely sort lists which depend on…
Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is…
In recent years, the success of deep learning has inspired many researchers to study the optimization of general smooth non-convex functions. However, recent works have established pessimistic worst-case complexities for this class…
The size of the \textit{smallest suffixient set} of positions of a string recently emerged as a new measure of string \textit{repetitiveness} -- a measure reflecting how much of repetitive content the string contains. We study how to…
While sorting is an important procedure in computer science, the argsort operator - which takes as input a vector and returns its sorting permutation - has a discrete image and thus zero gradients almost everywhere. This prohibits…
Many discrete minimization problems, including various versions of the shortest path problem, can be efficiently solved by dynamic programming (DP) algorithms that are "pure" in that they only perform basic operations, as min, max, +, but…
In this paper, we proposed a new efficient sorting algorithm based on insertion sort concept. The proposed algorithm called Bidirectional Conditional Insertion Sort (BCIS). It is in-place sorting algorithm and it has remarkably efficient…
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…
In this master thesis we analyze the complexity of sorting a set of strings. It was shown that the complexity of sorting strings can be naturally expressed in terms of the prefix trie induced by the set of strings. The model of computation…
We present a sorting algorithm for the case of recurrent random comparison errors. The algorithm essentially achieves simultaneously good properties of previous algorithms for sorting $n$ distinct elements in this model. In particular, it…
TimSort is an intriguing sorting algorithm designed in 2002 for Python, whose worst-case complexity was announced, but not proved until our recent preprint. In fact, there are two slightly different versions of TimSort that are currently…
In this paper we examine sorting on the assumption that we do not know in advance which way to sort a sequence of numbers and we set at work simple local comparison and swap operators whose repeating application ends up in sorted sequences.…
In this paper, a sorting technique is presented that takes as input a data set whose primary key domain is known to the sorting algorithm, and works with an time efficiency of O(n+k), where k is the primary key domain. It is shown that the…
We study faster algorithms for producing the minimum degree ordering used to speed up Gaussian elimination. This ordering is based on viewing the non-zero elements of a symmetric positive definite matrix as edges of an undirected graph, and…
The present paper is concerned with a recursive algorithm as a preprocessing step to find the convex hull of $n$ random points uniformly distributed in the plane. For such a set of points, it is shown that eliminating all but $O(\log n)$ of…
Reasoning over procedural sequences, where the order of steps directly impacts outcomes, is a critical capability for large language models (LLMs). In this work, we study the task of reconstructing globally ordered sequences from shuffled…
Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…
LearnedSort is a novel sorting algorithm that, unlike traditional methods, uses fast ML models to boost the sorting speed. The models learn to estimate the input's distribution and arrange the keys in sorted order by predicting their…
We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…
A determined algorithm is presented for solving the rSUM problem for any natural r with a sub-quadratic assessment of time complexity in some cases. In terms of an amount of memory used the obtained algorithm is the nlog^3(n) order. The…