相关论文: Parallel Integer Relation Detection: Techniques an…
An algorithm which either finds an nonzero integer vector ${\mathbf m}$ for given $t$ real $n$-dimensional vectors ${\mathbf x}_1,...,{\mathbf x}_t$ such that ${\mathbf x}_i^T{\mathbf m}=0$ or proves that no such integer vector with norm…
Let $\mathbf{x_1}, ..., \mathbf{x_t} \in \mathbb{R}^{n}$. A simultaneous integer relation (SIR) for $\mathbf{x_1}, ..., \mathbf{x_t}$ is a vector $\mathbf{m} \in \mathbb{Z}^{n}\setminus\{\textbf{0}\}$ such that $\mathbf{x_i}^T\mathbf{m} =…
Integer sorting is a fundamental problem in computer science. This paper studies parallel integer sort both in theory and in practice. In theory, we show tighter bounds for a class of existing practical integer sort algorithms, which…
Exactly solving multi-objective integer programming (MOIP) problems is often a very time consuming process, especially for large and complex problems. Parallel computing has the potential to significantly reduce the time taken to solve such…
An integer adder for integers in the binary representation is one of the basic operations of any digital processor. For adding two integers of N bits each, the serial adder takes as many clock ticks. For achieving higher speeds, parallel…
Usage of multiprocessor and multicore computers implies parallel programming. Tools for preparing parallel programs include parallel languages and libraries as well as parallelizing compilers and convertors that can perform automatic…
Integer relation algorithms can convert numerical results for Feynman integrals to exact evaluations, when one has reason to suspect the existence of reductions to linear combinations of a basis, with rational or algebraic coefficients.…
The using of quantum parallelism is often connected with consideration of quantum system with huge dimension of space of states. The n-qubit register can be described by complex vector with 2^n components (it belongs to n'th tensor power of…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
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.…
To every integer monic polynomial of degree m can be associated m integer sequences having interesting properties to the roots of the polynomial. These sequences can be used to find the real roots of any integer monic polynomial by using…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…
We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this…
Today's PCs can directly manipulate numbers not longer than 64 bits because the size of the CPU registers and the data-path are limited. Consequently, arithmetic operations such as addition, can only be performed on numbers of that length.…
We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring"…
We study parallel comparison-based algorithms for finding all equivalence classes of a set of $n$ elements, where sorting according to some total order is not possible. Such scenarios arise, for example, in applications, such as in…
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…
Many parallel algorithms which solve basic problems in computer science use auxiliary space linear in the input to facilitate conflict-free computation. There has been significant work on improving these parallel algorithms to be in-place,…
Many emerging computer applications require the processing of large numbers, larger than what a CPU can handle. In fact, the top of the line PCs can only manipulate numbers not longer than 32 bits or 64 bits. This is due to the size of the…
A* is a best-first search algorithm for finding optimal-cost paths in graphs. A* benefits significantly from parallelism because in many applications, A* is limited by memory usage, so distributed memory implementations of A* that use all…