Parallel Approximation Algorithms

Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

Design Algorithms for Doppler MTI and Filters (Using Chebyshev Approximation)

A New Parallel Matrix Multiplication Method Adapted on Fibonacci Hypercube Structure

The objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel matrix multiplication can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel matr...

Implementation of the direction of arrival estimation algorithms by means of GPU-parallel processing in the Kuda environment (Research Article)

Direction-of-arrival (DOA) estimation of audio signals is critical in different areas, including electronic war, sonar, etc. The beamforming methods like Minimum Variance Distortionless Response (MVDR), Delay-and-Sum (DAS), and subspace-based Multiple Signal Classification (MUSIC) are the most known DOA estimation techniques. The mentioned methods have high computational complexity. Hence using...

A New Approach to Solve N-Queen Problem with Parallel Genetic Algorithm

Over the past few decades great efforts were made to solve uncertain hybrid optimization problems. The n-Queen problem is one of such problems that many solutions have been proposed for. The traditional methods to solve this problem are exponential in terms of runtime and are not acceptable in terms of space and memory complexity. In this study, parallel genetic algorithms are proposed to solve...

Parallel Cost Approximation Algorithms for Differentiable Optimization

This paper presents a uniied analysis of decomposition algorithms for continuously diierentiable optimization problems deened on Cartesian products of convex feasible sets. The decomposition algorithms are analyzed using the framework of cost approximation algorithms. A convergence analysis is made for three decomposition algorithms: a sequential algorithm which encompasses the classical Gauss{...