关于实质本源蕴涵项的识别问题

本文揭示ＥＳＰＲＥＳＳＯ算法和Ｍｕｒｏｇａ等提出的求绝对最小算法中识别实质本源蕴涵项的方法具有近似的复杂度。文中还给出了一个在产生本源蕴涵项过程中识别实质本源项的算法。     

多输出逻辑函数最小化的一个算法

本文描述一个多输出逻辑函数的最小化算法。函数解中积项总数的多少被看作是衡量算法优劣的最重要指标。因此，我们努力使解中的积项被尽可能多的组成函数共享。本文求本源蕴涵项的方法与［１］是相似的。因此，本文也可看成是［１］向多输出函数的延伸。     

逻辑函数无冗余覆盖选择问题

逻辑函数的最小化算法可以分为两大步骤,产生本源蕴涵项和在这些蕴涵项中选择一个最小覆盖。提出一个适于大变量输入输出逻辑函数的实质项与相对冗余项的识别和选择近似最小覆盖的算法。Benchmark例题测试表明,算法具有理想的处理效果。     

逻辑函数的无冗余覆盖选择问题

逻辑函数的最小化算法可分为两大步骤：产生本源蕴涵项和在这些蕴涵项中选择一个最小覆盖。人说后者比前者更加困难,这的确是事实。我们这里提出一个无冗余和选择一个最小覆盖的算法。给定函数ｆ的一个本源覆盖Ｇ,首先将Ｇ分为三个子集：实质本源项子集Ｅ,完全冗余项子集Ｒ和相对冗余项子集Ｐ。然后在Ｐ中选择一个子集Ｐ＾＊,使Ｐ＾＊∪Ｅ为ｆ的一个近似最小覆盖。很明显,后一项任务比前者要复杂得多。所以,我们的讨论侧重于后     

逻辑函数绝对最小覆盖的改进算法

逻辑函数的绝对最小化算法存在的主要问题是运行时间过长和需要的存储空间过大。本文提出了一个从给定本源蕴涵项集合中抽出一个绝对最小覆盖的算法，而时间、空间的需求被大缩小了。     

基于编码算法的组合逻辑电路最优化软件的设计与实现

在组合电路综合领域,逻辑最小化对电路面积及性能起到至关重要的作用。文章提出了一个新的产生本源蕴涵项的算法,并开发了一个最优化软件MININT,实验表明,它在运算速度和存储性能上都是高效的。     

一种求解多值逻辑函数接近最小覆盖的算法

1.引言 本文研究Allen-Givone多值逻辑代数系统中的“积之和”形式的函数的简化算法。首先,在讨论符合目前多值逻辑函数实现特点的合理代价标准基础上,提出了一种折衷的代价标准,按着这个标准不求所有质蕴涵项集合,直接求解无冗余覆盖。这个算法以减少文字门的个数为依据,在确定某些质蕴涵项和实现文字数较少之间进行权衡,它在一个位     

大变量多输出逻辑函数实质项识别算法

在对Espresso算法进行分析改进的基础上，提出了一种基于全域识别的多输入多输出逻辑函数实质本源项、完全冗余项和相对冗余项生成算法，该算法通过对基于积项表示的多输入多输出逻辑函数的余因子计算来进行全域判断，根据全域判断结果来识别实质本源项、完全冗余项和相对冗余项，从而构成实质本源项集合、完全冗余项集合和相对冗余项集合。对基于二级SOP型的多输入多输出逻辑函数设计了多输入多输出逻辑函数优化识别软件系统，允许的最大输入变量数为128、最大输出变量数为256、最大输入输出变量总和为300、最大输入积项数为20 000。软件系统在Pentium 1.8GHz、512MB内存的计算机上通过了Benchmark例题的测试。     

全蕴涵三I算法的推理结果研究

Zadeh提出的CRI算法是模糊推理中运用最广泛的算法,但其逻辑语义不太清楚,也不具有还原性。王国俊教授提出的全蕴涵三I算法具有还原性,并在一定程度上解决了模糊推理的逻辑基础不够完善的问题。现在,全蕴涵三I算法已经获得了普遍的接受,并有许多学者对该算法进行了多种形式的推广。但全蕴涵三I算法及其改进算法在实际控制中都还未见成功的运用。对全蕴涵三I算法的推理结果进行了全面分析,指出全蕴涵三I算法存在的问题及其不能应用于实际控制的原因。     

大变量多输出逻辑函数实质项识别算法

在对Espresso算法进行分析改进的基础上,提出了一种基于全域识别的多输入多输出逻辑函数实质本源项、完全冗余项和相对冗余项生成算法,该算法通过对基于积项表示的多输入多输出逻辑函数的余因子计算来进行全域判断,根据全域判断结果来识别实质本源项、完全冗余项和相对冗余项,从而构成实质本源项集合、完全冗余项集合和相对冗余项集合.对基于二级SOP型的多输入多输出逻辑函数设计了多输入多输出逻辑函数优化识别软件系统,允许的最大输入变量数为128、最大输出变量数为256、最大输入输出变量总和为300、最大输入积项数为20 000.软件系统在Pentium 1.8GHz、512MB内存的计算机上通过了Benchmark例题的测试.     

Finding Optimal Ordering of Sparse Matrices for Column-Oriented Parallel Cholesky Factorization

In this paper, we consider the problem of finding fill-preserving sparse matrix orderings for parallel factorization. That is, given a large sparse symmetric and positive definite matrix A that has been ordered by some fill-reducing ordering, we want to determine a reordering that is appropriate in terms of preserving the sparsity and minimizing the cost to perform the Cholesky factorization in parallel. Past researches on this problem all are based on the elimination tree model, in which each node represents the task for factoring a column, and thus, can be seen as a coarse-grained task dependence model. To exploit more parallelism, Joseph Liu proposed a medium-grained task model, called the column task graph, and showed that it is amenable to the shared-memory supercomputers. Based on the column task graph, we devise a greedy reordering algorithm, and show that our algorithm can find the optimal ordering among the class of all fill-preserving orderings of the given sparse matrix A.     

基于超节点LDL分解的大规模结构计算

采用列压缩稀疏(Compressed Sparse Column,CSC)矩阵存储策略对矩阵LDL分解前进行填充元优化排序;基于消去树进行LDL符号分解,使之独立于数值分解,避免多余的内存消耗,减少不必要的数值运算.利用矩阵非零元的分布特性分析并实现超节点LDL分解算法,将稀疏矩阵的分解运算变为一系列稠密矩阵运算,并使用优化的BLAS函数库加速分解.测试表明:算法在成倍地提高计算速度的同时进一步降低内存消耗,适用于大规模的结构计算.     

基于试探性消除策略的改进ERRE算法

针对有效冗余阅读器消除算法（Efficient Redundant Reader Elimination,ERRE）存在对RFID网络拓扑结构要求高和需要设定用户自定义因子的不足,提出基于试探性消除策略的改进ERRE算法。该算法在ERRE算法的基础上加入试探性消除策略,提高算法在不同拓扑结构下运行的有效性;并删除性能函数和权重函数,设阅读器的邻居数与覆盖数的比值作为冗余阅读器判定值。最后,通过实例分析证明改进算法的有效性,并和算法RRE、LEO、ERRE进行仿真对比分析。实验结果表明,改进算法在继承ERRE算法优点的同时,可适用于任何拓扑结构的RFID网络,而且不需要设定用户自定义因子,避免了人为因素对实验结果可信度的影响。相较其他算法,改进算法可以有效消除更多冗余阅读器。     

Improving Parallel Ordering of Sparse Matrices Using Genetic Algorithms

In the direct solution of sparse symmetric and positive definite linear systems, finding an ordering of the matrix to minimize the height of the elimination tree (an indication of the number of parallel elimination steps) is crucial for effectively computing the Cholesky factor in parallel. This problem is known to be NP-hard. Though many effective heuristics have been proposed, the problems of how good these heuristics are near optimal and how to further reduce the height of the elimination tree remain unanswered. This paper is an effort for this investigation. We introduce a genetic algorithm tailored to this parallel ordering problem, which is characterized by two novel genetic operators, adaptive merge crossover and tree rotate mutation. Experiments showed that our approach is cost effective in the number of generations evolved to reach a better solution in reducing the height of the elimination tree.     

A fast LDL-factorization approach for large sparse positive definite system and its application to one-to-one marketing optimization computation

LDL-factorization is an efficient way of solving Ax=b for a large symmetric positive definite sparse matrix A.This paper presents a new method that further improves the efficiency of LDL-factorization.It is based on the theory of elimination trees for the factorization factor.It breaks the computations involved in LDL-factorization down into two stages:1) the pattern of nonzero entries of the factor is predicted,and 2) the numerical values of the nonzero entries of the factor are computed.The factor is stored using the form of an elimination tree so as to reduce memory usage and avoid unnecessary numerical operations.The calculation results for some typical numerical examples demonstrate that this method provides a significantly higher calculation efficiency for the one-to-one marketing optimization algorithm.     

基于Hopfield网络的多变量动态矩阵控制及其在精馏塔系统中的应用

利用Hopfield网络的优化计算功能求解有约束多变量动态知阵控制问题,算法简单,收敛性好,即或以用硬件实时实现,也可用数值积分求解,对Wood-Berry精馏塔的仿真表明了算法的有效性。     

求解正则式方程式集合的面向矩阵高斯主元消去法

本文在论述利用系数矩阵进行消元变换求解正则表达式方程式集合的高斯消去法的基础上，提出了一种选取系数矩阵中主元素进行消元变换求解正则表达式方程式集合的高斯主元素消去法，并给出易编程的算法。     

An optimal algorithm for Gaussian elimination of band matrices on an MIMD computer

This paper describes a parallel algorithm for the LU decomposition of band matrices using Gaussian elimination. The matrix dimension is n × n with 2r−1 diagonals. In the case when 1 r 2 p an optimal number of the processors, , is determined according to the equation . When 2 p r n a number of processors, p, statged by Veldhorst is adopted (see [7]). For band matrix with 2r-1 diagonals (1 r 2p) the task scheduling procedure with the aim to obtain maximal parallelism in system operation, i.e. good load balancing, is defined. The architecture of the system is of MIMD type. The connection between the processors is realised via a common bus. Communication and synchronization is performed by message passing technique.     

Improving the numerical stability and the performance of a parallel sparse solver

Coarse grain parallel codes for solving sparse systems of linear algebraic equations can be developed in several different ways. The following procedure is suitable for some parallel computers. A preliminary reordering of the matrix is first applied to move as many zero elements as possible to the lower left corner. After that the matrix is partitioned into large blocks and the blocks in the lower left corner contain only zero elements. An attempt to obtain a good load-balance is carried out by allowing the diagonal blocks to be rectangular.

While the algorithm based on the above ideas has good parallel properties, some stability problems may arise during the factorization because the pivotal search is restricted to the diagonal blocks. A simple a priori procedure has been used in a previous version in an attempt to stabilize the algorithm. In this paper it is shown that three enhanced stability devices can successfully be incorporated in the algorithm so that it is further stabilized and, moreover, the parallel properties of the original algorithm are preserved.

The first device is based on a dynamic check of the stability. In the second device a slightly modified reordering is used in an attempt to get more nonzero elements in the diagonal blocks (the number of candidates for pivots tends to increase in this situation and, therefore, there is a better chance to select more stable pivots). The third device applies a P⁵-like ordering as a secondary criterion in the basic reordering procedure. This tends to improve the reordering and the performance of the solver. Moreover, the device is stable, while the original P⁵ ordering is often unstable.

Numerical results obtained by using the three new devices are presented. The well-known sparse matrices from the Harwell-Boeing set are used in the experiments.     

凸多面体线消隐算法的研究与改进

为使三维形体有较强的立体感,物体因自身遮挡和物体间的相互遮挡产生的线段就必须被消除.在研究了三维几何形体消隐算法中的线消隐算法之后,针对传统的凸多面体线消隐算法存在计算量大、消隐时间长、效率低的缺点进行改进,在原来线消隐算法的基础上加入包围盒的最大最小测试方法和深度优先排序方法.算法使用C++编程实现,实验证明算法的时间复杂度由原来的N2降低为N,大大提高了消隐效率.