Related papers: MapReduce for Integer Factorization
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
MapReduce, the popular programming paradigm for large-scale data processing, has traditionally been deployed over tightly-coupled clusters where the data is already locally available. The assumption that the data and compute resources are…
The exponential growth of data in current times and the demand to gain information and knowledge from the data present new challenges for database researchers. Known database systems and algorithms are no longer capable of effectively…
Many matrices associated with fast transforms posess a certain low-rank property characterized by the existence of several block partitionings of the matrix, where each block is of low rank. Provided that these partitionings are known,…
MapReduce has become the de facto standard model for designing distributed algorithms to process big data on a cluster. There has been considerable research on designing efficient MapReduce algorithms for clustering, graph optimization, and…
With the increasing demand for high-performance and high-efficiency computing, cloud computing, especially serverless computing, has gradually become a research hotspot in recent years, attracting numerous research attention. Meanwhile,…
Current asymmetric cryptography is based on the principle that while classical computers can efficiently multiply large integers, the inverse operation, factorization, is significantly more complex. For sufficiently large integers, this…
Clustering analysis has received considerable attention in spatial data mining for several years. With the rapid development of the geospatial information technologies, the size of spatial information data is growing exponentially which…
Binary matrix factorisation is an essential tool for identifying discrete patterns in binary data. In this paper we consider the rank-k binary matrix factorisation problem (k-BMF) under Boolean arithmetic: we are given an n x m binary…
We show that $n$-bit integers can be factorized by independently running a quantum circuit with $\tilde{O}(n^{3/2})$ gates for $\sqrt{n}+4$ times, and then using polynomial-time classical post-processing. The correctness of the algorithm…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
We propose a novel factorization algorithm that leverages the theory underlying the SQUFOF method, including reduced quadratic forms, infrastructural distance, and Gauss composition. We also present an analysis of our method, which has a…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…
Large integer factorization is a prominent research challenge, particularly in the context of quantum computing. This holds significant importance, especially in information security that relies on public key cryptosystems. The classical…
The theoretical aspects of four integer factorization algorithms are discussed in details in this note. The focus is on the performances of these algorithms on the subset of hard to factor balanced integers N = pq, p < q < 2p. The running…
If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…
Designing fast and scalable algorithm for mining frequent itemsets is always being a most eminent and promising problem of data mining. Apriori is one of the most broadly used and popular algorithm of frequent itemset mining. Designing…
MapReduce is becoming the de facto framework for storing and processing massive data, due to its excellent scalability, reliability, and elasticity. In many MapReduce applications, obtaining a compact accurate summary of data is essential.…