Related papers: Improving the Space-Time Efficiency of Processor-O…
To obtain a better understanding of the trade-offs between various objectives, Bi-Objective Integer Programming (BOIP) algorithms calculate the set of all non-dominated vectors and present these as the solution to a BOIP problem.…
We introduce a novel framework for analyzing sorting algorithms in pairwise ranking prompting (PRP), re-centering the cost model around LLM inferences rather than traditional pairwise comparisons. While classical metrics based on comparison…
We consider the problem of sampling $n$ numbers from the range $\{1,\ldots,N\}$ without replacement on modern architectures. The main result is a simple divide-and-conquer scheme that makes sequential algorithms more cache efficient and…
In this paper we develop optimal algorithms in the binary-forking model for a variety of fundamental problems, including sorting, semisorting, list ranking, tree contraction, range minima, and ordered set union, intersection and difference.…
Although the matrix multiplication plays a vital role in computational linear algebra, there are few efficient solutions for matrix multiplication of the near-sparse matrices. The Sparse Approximate Matrix Multiply (SpAMM) is one of the…
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…
We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…
In this paper, we present novel deterministic algorithms for multiplying two $n \times n$ matrices approximately. Given two matrices $A,B$ we return a matrix $C'$ which is an \emph{approximation} to $C = AB$. We consider the notion of…
The polynomial multiplication problem has attracted considerable attention since the early days of computer algebra, and several algorithms have been designed to achieve the best possible time complexity. More recently, efforts have been…
A simple method for improving cache efficiency of serial and parallel explicit finite procedure with application to casting solidification simulation over three-dimensional complex geometries is presented. The method is based on division of…
We present a simple and powerful algorithm for parallel black box optimization called Successive Halving and Classification (SHAC). The algorithm operates in $K$ stages of parallel function evaluations and trains a cascade of binary…
This paper is a contribution to exploring and analyzing space-improvements in concurrent programming languages, in particular in the functional process-calculus CHF. Space-improvements are defined as a generalization of the corresponding…
Recently, reinforcement algorithms discovered new algorithms that really jump-started a wave of excitements and a flourishing of publications. However, there is little on implementations, applications, and, especially, no absolute…
Learning-augmented algorithms -- in which, traditional algorithms are augmented with machine-learned predictions -- have emerged as a framework to go beyond worst-case analysis. The overarching goal is to design algorithms that perform…
We consider the classical scheduling problem on parallel identical machines to minimize the makespan, and achieve the following results under the Exponential Time Hypothesis (ETH) 1. The scheduling problem on a constant number $m$ of…
This paper addresses the efficient computation of Jacobian matrices for programs composed of sequential differentiable subprograms. By representing the overall Jacobian as a chain product of the Jacobians of these subprograms, we reduce the…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
In order to find the outcome probabilities of quantum mechanical systems like the optical networks underlying Boson sampling, it is necessary to be able to compute the permanents of unitary matrices, a computationally hard task. Here we…
A definition for a class of asynchronous cellular arrays is proposed. An example of such asynchrony would be independent Poisson arrivals of cell iterations. The Ising model in the continuous time formulation of Glauber falls into this…