Related papers: New Sorting Algorithm Wave Sort (W-Sort)

We generalize the classical nuts and bolts problem to a setting where the input is a collection of $n$ nuts and $m$ bolts, and there is no promise of any matching pairs. It is not allowed to compare a nut directly with a nut or a bolt…

Derivative Free Optimization is known to be an efficient and robust method to tackle the black-box optimization problem. When it comes to noisy functions, classical comparison-based algorithms are slower than gradient-based algorithms. For…

We formalize a new paradigm for optimality of algorithms, that generalizes worst-case optimality based only on input-size to problem-dependent parameters including implicit ones. We re-visit some existing sorting algorithms from this…

We consider $(\epsilon,\delta)$-PAC maximum-selection and ranking for general probabilistic models whose comparisons probabilities satisfy strong stochastic transitivity and stochastic triangle inequality. Modifying the popular knockout…

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…

We continue the study of selection and sorting of $n$ numbers under the adversarial comparator model, where comparisons can be adversarially tampered with if the arguments are sufficiently close. We derive a randomized sorting algorithm…

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…

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness…

We study a fundamental model of online preference aggregation, where an algorithm maintains an ordered list of $n$ elements. An input is a stream of preferred sets $R_1, R_2, \dots, R_t, \dots$. Upon seeing $R_t$ and without knowledge of…

This paper explores adaptive variance reduction methods for stochastic optimization based on the STORM technique. Existing adaptive extensions of STORM rely on strong assumptions like bounded gradients and bounded function values, or suffer…

It is essential that all algorithms are exhaustively, somewhat, and intelligently evaluated. Nonetheless, evaluating the effectiveness of optimization algorithms equitably and fairly is not an easy process for various reasons. Choosing and…

We present numerical results for the probability of bad cases for Quicksort, i.e. cases of input data for which the sorting cost considerably exceeds that of the average. Dynamic programming was used to compute solutions of the recurrence…

Modern parcel logistic networks are designed to ship demand between given origin, destination pairs of nodes in an underlying directed network. Efficiency dictates that volume needs to be consolidated at intermediate nodes in typical…

In the online sorting problem, $n$ items are revealed one by one and have to be placed (immediately and irrevocably) into empty cells of a size-$n$ array. The goal is to minimize the sum of absolute differences between items in consecutive…

In this paper, we describe randomized Shellsort--a simple, randomized, data-oblivious version of the Shellsort algorithm that always runs in O(n log n) time and, as we show, succeeds in sorting any given input permutation with very high…

Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms…

A new algorithm, Guidesort, for sorting in the uniprocessor variant of the parallel disk model (PDM) of Vitter and Shriver is presented. The algorithm is deterministic and executes a number of (parallel) I/O operations that comes within a…

Many statistical problems and applications require repeated computation of order statistics, such as the median, but most statistical and programming environments do not offer in their main distribution linear selection algorithms. We…

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…

Recent work by Google DeepMind introduced assembly-optimized sorting networks that achieve faster performance for small fixed-size arrays (3-8). In this research, we investigate the integration of these networks as base cases in classical…