Parallel Reduction Method Research Articles

Uniqueness of Power Flow Solutions Using Graph-Theoretic Notions

This article extends the uniqueness theory in (Park <i>et al.</i>, 2021) and establishes general necessary and sufficient conditions for the uniqueness of <inline-formula><tex-math notation="LaTeX">$P$</tex-math></inline-formula>&#x2013;<inline-formula><tex-math notation="LaTeX">$\Theta$</tex-math></inline-formula> power flow solutions in an AC power system using some properties of the monotone regime and the power network topology. We show that the necessary and sufficient conditions can lead to tighter sufficient conditions for the uniqueness in several special cases. Our results are based on the existing notion of maximal girth and our new notion of maximal eye. Moreover, we develop a series&#x2013;parallel reduction method and search-based algorithms for computing the maximal eye and the maximal girth, which are necessary for the uniqueness analysis. Reduction to a single line using the proposed reduction method is guaranteed for 2-vertex-connected series&#x2013;parallel graphs. The relations between the parameters of the network before and after reduction are obtained. It is verified on real-world networks that the computation of the maximal eye can be reduced to the analysis of a much smaller power network, while the maximal girth is computed during the reduction process.

Experimental quality evaluation of lattice basis reduction methods for decorrelating low-dimensional integer least squares problems

Reduction can be important to aid quickly attaining the integer least squares (ILS) estimate from noisy data. We present an improved LLL algorithm with fixed complexity by extending a parallel reduction method for positive definite quadratic forms to lattice vectors. We propose the minimum angle of a reduced basis as an alternative quality measure of orthogonality, which is intuitively more appealing to measure the extent of orthogonality of a reduced basis. Although the LLL algorithm and its variants have been widely used in practice, experimental simulations were only carried out recently and limited to the quality measures of the Hermite factor, practical running behaviors and reduced Gram-Schmidt coefficients. We conduct a large scale of experiments to comprehensively evaluate and compare five reduction methods for decorrelating ILS problems, including the LLL algorithm, its variant with deep insertions and our improved LLL algorithm with fixed complexity, based on six quality measures of reduction. We use the results of the experiments to investigate the mean running behaviors of the LLL algorithm and its variants with deep insertions and the sorted QR ordering, respectively. The improved LLL algorithm with fixed complexity is shown to perform as well as the LLL algorithm with deep insertions with respect to the quality measures on length reduction but significantly better than this LLL variant with respect to the other quality measures. In particular, our algorithm is of fixed complexity, but the LLL algorithm with deep insertions could seemingly not be terminated in polynomial time of the dimension of an ILS problem. It is shown to perform much better than the other three reduction methods with respect to all the six quality measures. More than six millions of the reduced Gram-Schmidt coefficients from each of the five reduction methods clearly show that they are not uniformly distributed but depend on the reduction algorithms used. The simulation results of the reduced Gram-Schmidt coefficients have clearly shown that our improved LLL algorithm tends to produce small reduced Gram-Schmidt coefficients near zero with a larger probability and large reduced Gram-Schmidt coefficients near both ends of 0.5 and −0.5 with a smaller probability.

Development of parallel explicit finite element sheet forming simulation system based on GPU architecture

Sheet forming simulation is very important for vehicle body design. Due to the increase of complexity and scale of the CAE model, a tradeoff between the accuracy and efficiency become the bottleneck for application. Therefore, a parallel explicit finite element (FE) based on graphics processing unit (GPU) architecture for sheet forming is developed. Implementation details with computer unified device architecture (CUDA) are considered in this work. A pre-index strategy is suggested for parallelization of nodal force assembling. Parallel reduction method is introduced to calculation of the global time step. To ensure the reliability and accuracy of the GPU-based program, double precision floating and intrinsic functions are implemented for the explicit FE computing. The simulation results based on a commercial NVIDIA GTX285 device can obtain about 27X speedup than on a Intel Q8200 CPU, which demonstrates the efficiency of the parallel sheet forming simulation system.

The call-by-value λµ∧∨-calculus

In this paper, we introduce the $λ μ ^{∧∨}$ - call-by-value calculus and we give a proof of the Church-Rosser property of this system. This proof is an adaptation of that of Andou (2003) which uses an extended parallel reduction method and complete development.

Data partitioning‐based parallel irregular reductions

AbstractDifferent parallelization methods for irregular reductions on shared memory multiprocessors have been proposed in the literature in recent years. We have classified all these methods and analyzed them in terms of a set of properties: data locality, memory overhead, exploited parallelism, and workload balancing. In this paper we propose several techniques to increase the amount of exploited parallelism and to introduce load balancing into an important class of these methods. Regarding parallelism, the proposed solution is based on the partial expansion of the reduction array. Load balancing is discussed in terms of two techniques. The first technique is a generic one, as it deals with any kind of load imbalance present in the problem domain. The second technique handles a special case of load imbalance which occurs whenever a large number of write operations are concentrated on small regions of the reduction arrays. Efficient implementations of the proposed optimizing solutions for a particular method are presented, experimentally tested on static and dynamic kernel codes, and compared with other parallel reduction methods. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Confluency and strong normalizability of call-by-value [formula omitted]-calculus

This paper proves the confluency and the strong normalizability of the call-by-value λμ-calculus with the domain-free style. The confluency of the system is proved by improving the parallel reduction method of Baba et al. The strong normalizability is proved by using the modified CPS-translation, which preserves the typability and the reduction relation. This paper defines the class of the reductions whose strictness is preserved by the modified CPS-translation to prove the strong normalizability.