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Recent advances in Retrieval-Augmented Generation (RAG) systems have popularized semantic chunking, which aims to improve retrieval performance by dividing documents into semantically coherent segments. Despite its growing adoption, the…
We design and implement parallel prefix sum (scan) algorithms using Ascend AI accelerators. Ascend accelerators feature specialized computing units: the cube units for efficient matrix multiplication and the vector units for optimized…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…
We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query…
The growth in the use of computationally intensive statistical procedures, especially with Big Data, has necessitated the usage of parallel computation on diverse platforms such as multicore, GPU, clusters and clouds. However, slowdown due…
The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…
Besides tensor contractions, one of the most pronounced computational bottlenecks in the non-orthogonally spin-adapted forms of the quantum chemistry methods CCSDT and CCSDTQ, and their approximate forms---including CCSD(T) and…
In this paper, we explore how numerical calculations can be accelerated by implementing several numerical methods of fractional-order systems using parallel computing techniques. We investigate the feasibility of parallel computing…
Priority queues with parallel access are an attractive data structure for applications like prioritized online scheduling, discrete event simulation, or branch-and-bound. However, a classical priority queue constitutes a severe bottleneck…
Serial and parallel algorithms for simulation of tandem queueing systems with infinite buffers are presented, and their performance is examined. It is shown that the algorithms which are based on a simple computational procedure involve low…
Polyspectral estimation is a problem of great importance in the analysis of nonlinear time series that has applications in biomedical signal processing, communications, geophysics, image, radar, sonar and speech processing, etc. Higher…
This paper investigates co-scheduling algorithms for processing a set of parallel applications. Instead of executing each application one by one, using a maximum degree of parallelism for each of them, we aim at scheduling several…
Using (a,b)-trees as an example, we show how to perform a parallel split with logarithmic latency and parallel join, bulk updates, intersection, union (or merge), and (symmetric) set difference with logarithmic latency and with information…
Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…
In typical black-box optimization applications, the available computational budget is often allocated to a single algorithm, typically chosen based on user preference with limited knowledge about the problem at hand or according to some…
Classical optimization algorithms in machine learning often take a long time to compute when applied to a multi-dimensional problem and require a huge amount of CPU and GPU resource. Quantum parallelism has a potential to speed up machine…
We show that the sum of a sequence of integers can be computed in linear time on a Turing machine. In particular, the most obvious algorithm for this problem, which appears to require quadratic time due to carry propagation, actually runs…
In the classic sequential testing problem, we are given a system with several components each of which fails with some independent probability. The goal is to identify whether or not some component has failed. When the test costs are…
CRCs have desirable properties for effective error detection. But their software implementation, which relies on many steps of the polynomial division, is typically slower than other codes such as weaker checksums. A relevant question is…