Related papers: Analysis of Quickselect under Yaroslavskiy's Dual-…
Using non-linear difference equations, combined with symbolic computations, we make a detailed study of the running times of numerous variants of the celebrated Quicksort algorithms, where we consider the variants of single-pivot and…
Recently, Aum\"uller and Dietzfelbinger proposed a version of a dual-pivot quicksort, called "Count", which is optimal among dual-pivot versions with respect to the average number of key comparisons required. In this note we provide further…
Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…
Sorted data is usually easier to compress than unsorted permutations of the same data. This motivates a simple compression scheme: specify the sorted permutation of the data along with a representation of the sorted data compressed…
We consider the fundamental problem of internally sorting a sequence of $n$ elements. In its best theoretical setting QuickMergesort, a combination Quicksort with Mergesort with a Median-of-$\sqrt{n}$ pivot selection, requires at most $n…
As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine…
We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…
In this article, bipartite ranking, a statistical learning problem involved in many applications and widely studied in the passive context, is approached in a much more general \textit{active setting} than the discrete one previously…
This paper addresses the anytime sorting problem, aiming to develop algorithms providing tentative estimates of the sorted list at each execution step. Comparisons are treated as steps, and the Spearman's footrule metric evaluates…
We consider a simple approach to solving assortment optimization under the random utility maximization model. The approach uses Monte-Carlo simulation to construct a ranking-based choice model that serves as a proxy for the true choice…
The weak limit of the normalized number of comparisons needed by the Quicksort algorithm to sort n randomly permuted items is known to be determined implicitly by a distributional fixed-point equation. We give an algorithm for perfect…
Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard average-case analysis is ammenable to this method. Here we…
Modern statistical analysis often encounters datasets with large sizes. For these datasets, conventional estimation methods can hardly be used immediately because practitioners often suffer from limited computational resources. In most…
I discuss the new dual-pivot Quicksort that is nowadays used to sort arrays of primitive types in Java. I sketch theoretical analyses of this algorithm that offer a possible, and in my opinion plausible, explanation why (a) dual-pivot…
Because of unmatched improvements in CPU performance, memory transfers have become a bottleneck of program execution. As discovered in recent years, this also affects sorting in internal memory. Since partitioning around several pivots…
We present sorting algorithms that represent the fastest known techniques for a wide range of input sizes, input distributions, data types, and machines. A part of the speed advantage is due to the feature to work in-place. Previously, the…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…
Sorting is a foundational primitive in modern data processing, influencing the execution speed of high-performance data pipelines. However, the algorithmic landscape is currently bifurcated by a pervasive "Stability Tax": practitioners must…
Survival analysis is a crucial semi-supervised task in machine learning with numerous real-world applications, particularly in healthcare. Currently, the most common approach to survival analysis is based on Cox's partial likelihood, which…
In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each…