Related papers: Average Case Analysis of Java 7's Dual Pivot Quick…
This paper presents RevOrder, a novel technique aimed at improving arithmetic operations in large language models (LLMs) by reversing the output digits in addition, subtraction, and n-digit by 1-digit (nD by 1D) multiplication tasks. Our…
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…
We consider a recursive record-filtering procedure, which we informally call Disappear-Sort. Let $D_n$ denote the random variable giving the required number of passes in Disappear-Sort to eliminate a sequence of length $n$ sampled as i.i.d.…
A perturbation technique can be used to simplify and sharpen A. C. Yao's theorems about the behavior of shellsort with increments $(h,g,1)$. In particular, when $h=\Theta(n^{7/15})$ and $g=\Theta(h^{1/5})$, the average running time is…
signSGD is popular in nonconvex optimization due to its communication efficiency. Yet, existing analyses typically assume data are sampled with replacement in each iteration, contradicting a common practical implementation where data are…
The quantum permutation algorithm provides computational speed-up over classical algorithms in determining the parity of a given cyclic permutation. For its $n$-qubit implementations, the number of required quantum gates scales…
With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms…
We give algorithms to accelerate the computation of deterministic finite automata (DFA) by calculating the state of a DFA n positions ahead utilizing a reverse scan of the next n characters. Often this requires scanning fewer than n…
Much more attention has been paid to unsupervised feature selection nowadays due to the emergence of massive unlabeled data. The distribution of samples and the latent effect of training a learning method using samples in more effective…
Quicksort algorithm with Hoare's partition scheme is traditionally implemented with nested loops. In this article, we present loop programming and refactoring techniques that lead to simplified implementation for Hoare's quicksort algorithm…
Learning an ordering of items based on pairwise comparisons is useful when items are difficult to rate consistently on an absolute scale, for example, when annotators have to make subjective assessments. When exhaustive comparison is…
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…
Frequently, randomly organized data is needed to avoid an anomalous operation of other algorithms and computational processes. An analogy is that a deck of cards is ordered within the pack, but before a game of poker or solitaire the deck…
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform…
Optimizing smooth convex functions in stochastic settings, where only noisy estimates of gradients and Hessians are available, is a fundamental problem in optimization. While first-order methods possess a low per-iteration cost, their…
We study sorting by queues that can rearrange their content by applying permutations from a predefined set. These new sorting devices are called shuffle queues and we investigate those of them corresponding to sets of permutations defining…
Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method and the weighted Jacobi method, exhibit simplicity in their…
Sorting is a fundamental and well studied problem that has been studied extensively. Sorting plays an important role in the area of databases, as many queries can be served much faster if the relations are first sorted. One of the most…
While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based…
When algorithms for sorting and searching are applied to keys that are represented as bit strings, we can quantify the performance of the algorithms not only in terms of the number of key comparisons required by the algorithms but also in…