并行算法

The topics are divided into three parts: the first part introduced the basic concepts of algorithms, mathematical algorithms and algorithms based on complexity analysis scheduling problem for the second part of the problem and plans to discuss a variety of existing algorithms, and describes the design of commonly used algorithms including sub-rule law, greedy method, dynamic programming, backtracking and branch and bound method, and describes the complexity of the calculation, as well as NP-complete problem the third part of the model on parallel computing and parallel algorithm design techniques.

全书分为3个部分：第一部分介绍算法的基本概念、算法的数学基础以及算法复杂度分析；第二部分针对排序问题和图的问题，讨论各种已有的算法，并介绍常用的算法设计方法包括分治法、贪心法、动态规划法、回溯法和分支限界法，并介绍了计算的复杂性以及NP完全问题；第三部分讲述并行计算模型和并行算法设计技术。

A parallel algorithm for certain real symmetric block-tridiagonal linear systems on distributed-memory multicomputers is proposed. This algorithm is based on the block factorization of the coefficient matrix. This algorithm is used to solving the block-tridiagonal linear systems resulted from the finite difference approximation to Poisson's equation with Dirichlet boundary conditions. Then we get a parallel algorithm which speedup tends to linear speedup.

7研究了一类实对称块三对角线性方程组的分布式并行求解，提出了一种基于块矩阵分解的高效分布式并行算法，将其应用于求解带Dirichlet边界条件的Poisson方程导出的块三对角线性方程组，得到加速比趋于线性加速比的分布式并行算法，理论上说，这也是并行算法的理想情况。

The main contributions of this dissertation are In chapter 2, we propose a scientific visualization system modal which is based on large-format display technology and Client-Commware-Server structure. In chapter 3 and chapter 4, we accomplish two large-scale scientific visualization systems. In chapter 5 and chapter 6, we propose HFFT on hexagon and parallel dodecahedron domains, and reduce the computational complexity from O and O to O and O . Lastly, we propose a parallel HFFT on distributed memory computers.

本文的主要贡献如下：提出了使用大屏幕显示技术、适用于大规模科学计算可视化系统的Client-Commware-Server模型；实现了油藏数值模拟和分子模拟两个大规模科学计算的可视化系统；给出了二维三方向六边形区域、三维四方向十二面体区域上的HFFT算法，将变换的计算复杂度分别从直接计算的O和O量级降到了快速算法的O和O量级；最后，本文给出了一种基于分布式存储的并行HFFT算法，并对影响、提高并行算法的若干因素进行了分析。

In this paper, combining the technique of parallel computation with the numerical method of 3D eddy current field, we designed the algorithms of generating mesh, forming finite element equations and solving them in parallel on a shared memory multiprocessor (SGI Challenge L 8 CPUs), and presented a concrete and effective method.

本文将并行计算技术和三维涡流场计算方法相结合，对三维涡流场有限元分析的并行处理技术进行了细致的研究，设计了基于共享内存并行计算机(SGI Challenge L 8 CPUs)的网格剖分并行算法和三维涡流场有限元方程形成和求解的并行算法，为数值求解实际三维涡流问题提供了一种有效途径和具体方法。

To find the minimum of energy function E is a part of work in the test generation based on neural network.

给出了神经网络测试生成的遗传进化方法的并行实现算法；提出了异步拟牛顿法、异步割线法和异步区间算法等三种异步并行算法，并对每一算法的收敛性及收敛效率做了分析，为神经网络测试生成方法在多机并行系统上的仿真实现提供了新的途径。

The problem of huge numbers of datas are disposed in the process of disposed three-dimensional laser scanning datas, so on the base of carefully analszing the serial algorithm of plane segmentation and multiple datasets registration in the process of disposing three-dimensional laser scan datas, according to the method of parallel programming basing on MPI, the paper used the right means of datas distributing to design and realize the parrel algorithm of plane segmentation and multiple datasets registration.

本文针对三维激光扫描数据处理过程中所处理的数据量大这一问题，在认真分析了三维激光扫描数据处理过程中平面分割和多视点配准串行算法的基础上，根据基于MPI并行程序设计方法，采用合适的数据分配方案，设计了平面分割和多视点配准的并行算法，并给出了效果图，以及并行算法加速比和效率的实际数据，最后对并行算法效果进行了分析。

Then based on the analysis of running time of binary algorithm and its imroved variant, I present a parallel algorithm of scalar multiplication, and analyze the running time of that parallel algorithm.

通过分析二进制算法及作为其改进算法的2~T -ary算法、加减链算法的运行时间的影响因素，论文继而提出了将2~T -ary算法并行化的算法，并对该并行算法的运行时间进行了理论上的分析。

Design random number generators with good independence and good uniformity is the key in reliability parallel simulation. Four algorithms of parallel random number generators are introduced. They are segmented parallel algorithm and leapfrog parallel algorithm of multiplicative congruential generator and generalized feedback shift register generator, parallel algorithm of lagged Fibonacci generator, and parallel algorithm of combined generator.

可靠性并行仿真的关键问题是设计独立性、均匀性良好的并行伪随机数序列，本文给出了基于分段并行算法和跳跃式并行算法的乘同余发生器、GFSR发生器和延迟Fibonacci发生器、组合发生器等的并行算法，组合发生器能够产生周期为2.3×10〓的伪随机数序列，且品质良好。

Moreover, A hybrid algorithm, ALHybrid, which is made of the algorithm LIDBSO and the algorithm AprioriIpv, is designed. Two algorithm, MQC_Apriori and MQC_LIDBSO, are given to mining multiple level quantitative association rules with item constrains. Two algorithm, PMARⅡ and PMARⅢ, which are based on different sequential mining algorithms, are given for parallelling mining association rules. In order to solve the mining association rules problem when we add a set of data to a database or delete a set of data from a database, two incremental updating algorithm, EUAR and EUAR, are given. Three incremental updating algorithm for association rules mining, DIUAⅠ, DIUAⅡ and DIUAⅢ, are dedigned to solve the three kinds of association rules incremental updating problem in distributed databases.

另外，文中还设计了一个算法LIDBSO与算法AprioriIpv相结合的混合采掘算法ALHybrid；对于多层次、带约束、多值属性关联规则的采掘问题，给出了两个采掘算法：算法MQC_Apriori和算法MQC_LIDBSO；在关联规则的并行采掘方面，还设计了两个基于不同顺序关联规则采掘算法的并行算法：算法PMARⅡ和算法PMARⅢ；在关联规则的增量式更新问题上，还给出了两个改进算法：算法EUAR和算法EUARˉ，分别用于解决当数据库增加或删除一个数据集合时的关联规则增量式更新问题；针对分布式数据库中的关联规则增量式更新的三类问题，提出了三个增量式更新算法：算法DIUA Ⅰ、算法DIUAⅡ和算法DIUAⅢ。

Based on these, parallel computing problem of matrix tensor product is discussed, some parallel computing models are presented, the algorithm complexity is analyzed, and the thought and process are elaborated by an example. block matrix ; tensor product ; permuted similar ; parallel algorithms ; computational complexity

文献〔l论述了Cannon算法在工作站机群上的实现，文献[2]提出了一种基于对角划分的并行算法，文献〔3〕提出了在分布式环境下并行求解对称带状矩阵特征值问题的并行二分/多分法及其改进，文献41给出了稠密对称矩阵三对角化的MPI+OpenMP混合并行算法，还有著名的Cannon

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。