Related papers: Modular SIMD arithmetic in Mathemagix
In this paper, we present fast algorithms for the product of two multivariate polynomials in sparse representation. The bit complexity of our algorithms are studied in detail for various types of coefficients, and we derive new complexity…
In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
This paper presents a fast and effective computer algebraic method for analyzing and verifying non-linear integer arithmetic circuits using a novel algebraic spectral model. It introduces a concept of algebraic spectrum, a numerical form of…
We describe an efficient implementation of a hierarchy of algorithms for multiplication of dense matrices over the field with two elements (GF(2)). In particular we present our implementation -- in the M4RI library -- of Strassen-Winograd…
Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for…
We present Matrix Distributed Processing, a C++ library for fast development of efficient parallel algorithms. MDP is based on MPI and consists of a collection of C++ classes and functions such as lattice, site and field. Once an algorithm…
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…
We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…
Montgomery modular multiplication is widely-used in public key cryptosystems (PKC) and affects the efficiency of upper systems directly. However, modulus is getting larger due to the increasing demand of security, which results in a heavy…
This paper surveys the trend of leveraging machine learning to solve mixed integer programming (MIP) problems. Theoretically, MIP is an NP-hard problem, and most of the combinatorial optimization (CO) problems can be formulated as the MIP.…
Linear Programming is now included in Algorithm undergraduate and postgraduate courses for Computer Science majors. It is possible to teach interior-point methods directly with just minimal knowledge of Algebra and Matrices.
We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect…
We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.
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…
This paper presents an algorithm for the integer multiplicative inverse (mod $2^w$) which completes in the fewest cycles known for modern microprocessors, when using the native bit width $w$ for the modulus $2^w$. The algorithm is a…
In the work we discuss the benefit of using bitwise operations in programming. Some interesting examples in this respect have been shown. What is described in detail is an algorithm for sorting an integer array with the substantial use of…
Augmentation methods for mixed-integer (linear) programs are a class of primal solution approaches in which a current iterate is augmented to a better solution or proved optimal. It is well known that the performance of these methods, i.e.,…
In this work, we study the problem of monotone non-submodular maximization with partition matroid constraint. Although a generalization of this problem has been studied in literature, our work focuses on leveraging properties of partition…
In recent years, with the rapid development of electro-optic modulators, optical computing has become a potential excellent candidate for various computing tasks. New structures and devices for optical computing are emerging one after…