Related papers: Engineering Faster Sorters for Small Sets of Items
Efficient learning from demonstration for long-horizon tasks remains an open challenge in robotics. While significant effort has been directed toward learning trajectories, a recent resurgence of object-centric approaches has demonstrated…
Quicksort on the fly returns the input of $n$ reals in increasing natural order during the sorting process. Correctly normalized the running time up to returning the l-th smallest out of n seen as a process in l converges weakly to a…
While Transformers have achieved remarkable success in LLMs through superior scalability, their application in industrial-scale ranking models remains nascent, hindered by the challenges of high feature sparsity and low label density. In…
Indexing of static and dynamic sets is fundamental to a large set of applications such as information retrieval and caching. Denoting the characteristic vector of the set by B, we consider the problem of encoding sets and multisets to…
We introduce and analyse a new, extremely simple, randomised sorting algorithm: - choose a pair of indices $\{i, j\}$ according to some distribution $q$; - sort the elements in positions $i$ and $j$ of the array in ascending order. Choosing…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
The "ordered set" abstract data type with operations "insert", "erase", "find", "min", "max", "next" and "prev" is ubiquitous in computer science. It is usually implemented with red-black trees, $B$-trees, or $B^+$-trees. We present our…
We consider the classical problem of sorting an input array containing $n$ elements, where each element is described with a $k$-bit comparison-key and a $w$-bit payload. A long-standing open problem is whether there exist $(k + w) \cdot o(n…
Deep learning models have proven to be exceptionally useful in performing many machine learning tasks. However, for each new dataset, choosing an effective size and structure of the model can be a time-consuming process of trial and error.…
This article introduces an adaptive sorting algorithm that can relocate elements accurately by substituting their values into a function which we name it the guessing function. We focus on building this function which is the mapping…
Prehensile object rearrangement in cluttered and confined spaces has broad applications but is also challenging. For instance, rearranging products in a grocery shelf means that the robot cannot directly access all objects and has limited…
Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical…
The sorting problem is one of the most relevant problems in computer science. Within the scope of modern computer science it has been studied for more than 70 years. In spite of these facts, new sorting algorithms have been developed in…
Deep neural networks have gained tremendous popularity in last few years. They have been applied for the task of classification in almost every domain. Despite the success, deep networks can be incredibly slow to train for even moderate…
Quicksort is an instructive classroom approach to parallel sorting on distributed memory parallel computers with many opportunities for illustrating specific implementation alternatives and tradeoffs with common communication interfaces…
Many production-grade algorithms benefit from combining an asymptotically efficient algorithm for solving big problem instances, by splitting them into smaller ones, and an asymptotically inefficient algorithm with a very small…
Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparison-based sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However,…
Visually sorted grid layouts provide an efficient method for organizing high-dimensional vectors in two-dimensional space by aligning spatial proximity with similarity relationships. This approach facilitates the effective sorting of…
Reductions---rules that reduce input size while maintaining the ability to compute an optimal solution---are critical for developing efficient maximum independent set algorithms in both theory and practice. While several simple reductions…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…