Related papers: Average Cost of QuickXsort with Pivot Sampling

In the first place, a novel, yet straightforward in-place integer value-sorting algorithm is presented. It sorts in linear time using constant amount of additional memory for storing counters and indices beside the input array. The…

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…

Sorting is one of the most basic algorithms, and developing highly parallel sorting programs is becoming increasingly important in high-performance computing because the number of CPU cores per node in modern supercomputers tends to…

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 propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…

We introduce a fast and explainable clustering method called CLASSIX. It consists of two phases, namely a greedy aggregation phase of the sorted data into groups of nearby data points, followed by the merging of groups into clusters. The…

Clustering of data points is a fundamental tool in data analysis. We consider points $X$ in a relaxed metric space, where the triangle inequality holds within a constant factor. The {\em cost} of clustering $X$ by $Q$ is $V(Q)=\sum_{x\in X}…

Scaling clustering algorithms to massive data sets is a challenging task. Recently, several successful approaches based on data summarization methods, such as coresets and sketches, were proposed. While these techniques provide provably…

The success of deep learning hinges on enormous data and large models, which require labor-intensive annotations and heavy computation costs. Subset selection is a fundamental problem that can play a key role in identifying smaller portions…

Data-driven algorithm selection is a powerful approach for choosing effective heuristics for computational problems. It operates by evaluating a set of candidate algorithms on a collection of representative training instances and selecting…

It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…

Circuit routing has been a historically challenging problem in designing electronic systems such as very large-scale integration (VLSI) and printed circuit boards (PCBs). The main challenge is that connecting a large number of electronic…

Several real-world classification problems are example-dependent cost-sensitive in nature, where the costs due to misclassification vary between examples and not only within classes. However, standard classification methods do not take…

In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\alpha \in [0,1)$.…

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…

Given the continuous increase in dataset sizes and the complexity of forecasting models, the trade-off between forecast accuracy and computational cost is emerging as an extremely relevant topic, especially in the context of ensemble…

The softmax function is a cornerstone of multi-class classification, integral to a wide range of machine learning applications, from large-scale retrieval and ranking models to advanced large language models. However, its computational cost…

Feature selection is an important preprocessing step in machine learning and data mining. In real-world applications, costs, including money, time and other resources, are required to acquire the features. In some cases, there is a test…

This version is ***superseded*** by a full version that can be found at http://www.itu.dk/people/pagh/papers/mining-jour.pdf, which contains stronger theoretical results and fixes a mistake in the reporting of experiments. Abstract:…

The mean completion time of a stochastic process may be rendered finite and minimised by a judiciously chosen restart protocol, which may either be stochastic or deterministic. Here we study analytically an arbitrary stochastic search…