具有次限制的最小树问题

F.Glover和D.Klingman在[2]中给出了予先确定的一个点x具有固定次数为k的最小树算法。 本文给出了任意m个互不关联点具有次数限制的最小树问题的算法.算法的基础是线性规划的对偶理论。     

最小树问题的全部解

<正> 以某些实际问题(如管道设计、通讯网建设等)为背景,图论中的最小树问题引起人们的广泛兴趣.自从 Kruskal 提出三种基本的构造法以后,各种算法实现途径相继出现,使这一问题得到完满的解决.然而,实际问题往往不能满足于求出一个最小树,而希望兼顾其它目标,在若干最小树中进行再选择.这就要求我们讨论最小树问题的全部解.在已有文献中,求全部支撑树已有较成熟的算法,尤其是文献[4]提供的算法可以将全部支撑树按权的大小依次列出.从理论上说,可以认为这些结果已经包含了求全部最小树问题.作为另一种途径,本文将着重讨论最小树问题全部解的性质,并由此建立求全部解的广探法(求全部支撑树的 Mayeda-Seshu 算法的推广).     

第一阶段原有单纯形和对偶单纯形算法的计算比较

线性最优化广泛应用于经济与管理的各个领域.在线性规划问题的求解中,如果一个初始基本可行解没有直接给出,则常采用经典的两阶段法求解.对含有"≥"不等式约束的线性规划问题,讨论了第一阶段原有单纯形法和对偶单纯形法两种算法形式,并根据第一阶段问题的特点提出了改进的对偶单纯形枢轴准则.最后,通过大规模数值试验对两种算法进行计算比较,结果表明,改进后的对偶单纯形算法在计算效率上明显优于原有单纯形算法.     

一种原始——对偶单纯形算法的枢轴准则选择

Curet曾提出了一种有趣的原始一对偶技术,在优化对偶问题的同时单调减少原始不可行约束的数量,当原始可行性产生时也就产生了原问题的最优解.然而该算法需要一个初始对偶可行解来启动,目标行的选择也是灵活、不确定的.根据Curet的原始一对偶算法原理,提出了两种目标行选择准则,并通过数值试验进行比较和选择.对不存在初始对偶可行解的情形,通过适当改变目标函数的系数来构造一个对偶可行解,以求得一个原始可行解,再应用原始单纯形算法求得原问题的最优解.数值试验对这种算法的计算性能进行验证,通过与经典两阶段单纯形算法比较,结果表明,提出的算法在大部分问题上具有更高的计算效率.     

最小树的层次算法及全部最小树动态结构

最小树问题在国民经济中有着广泛的应用。本文提出不同于著名的kruskal算法[1]及其他算法的层次算法,并推导出揭示最小树不变量的枝杈确定性以及边可作为最小树树枝的充要条件,最后得出全部最小树的动态结构。由于实际选用最小树时还经常需要兼顾其它具体     

Ford-Fulkerson算法与嵌入图中的短圈

关于嵌入图中最短圈的多项式算法的存在性问题,是由Thomassen最早提出的.本文通过改进的Ford-Fulkerson算法,可以得到最短割算法.另一方面,通过定义嵌入图的几何对偶图及其相应的嵌入系统,得到几何对偶图中的可分离圈就对应于原图中的割;反之,若几何对偶图中的割在原图中对应于-个圈,那么该圈一定可分离.从而在射影平面上解决了Mohar与Thomassen关于是否存在多项式算法寻找短圈的问题.对于-般曲面上嵌入图,只要它的面宽度充分大,那么同样有多项式算法发现最短可收缩圈.     

基于最陡边规则的亏基对偶Ⅰ阶段算法

将摄动算法和亏基原始单纯形算法相结合,采用最陡边的列主元规则,以充分发挥这两种算法的优势,从而为亏基对偶单纯形算法提供一个新的I阶段算法,以使其进一步克服了退化所带来的困扰.初步的数值试验表明,所提出的算法能有效地减少总迭代次数,其效率不仅远远优于传统的原始两阶段单纯形算法,且优于原有的亏基原始单纯形算法,是一个非常吸引人而充满希望的新尝试.     

基于亏基的摄动原始单纯形Ⅰ阶段算法

通过摄动技术来使问题强制获得对偶可行性,执行亏基对偶单纯形算法得到一个原始可行基,并采用修正的主元规则,以充分发挥这两种算法的优势,从而为亏基原始单纯形算法提供一个新的I阶段算法,以使其进一步克服退化所带来的困扰.初步的数值试验表明,亏基和摄动两种算法优势的结合,能有效地克服退化的影响,能有效地减少总迭代次数和运行时间,其效率远远优于传统两阶段单纯形算法.     

向量机上最优并行矩阵乘法算法

本文给出两种在向量计算机上计算n阶矩阵乘积的并行算法: 1)最优内积算法. 处理机台数 ρ_1=n~3/log_2n,     

Schwarz 算法的 Lions 框架与异步并行算法的收敛性证明

经典的Schwarz算法,早在1870年就提出了,是求解不规则椭圆型方程的交替法.本世纪苏联学者等又在变分框架下论证了收敛性.近年来以 Schwarrz算法为基础的区域分解算法,发展十分活跃,当前该方法正与并行算法,预处理,快速直接解,多水平及多层网格技术结合,成为计算数学领域内最有前途一个分支.虽然表面看 Schwarz 算法不是并行的,但康立山等打破了分解区域为两子域的     

An architecture independent study of parallel segment trees

We study the computation, communication and synchronization requirements related to the construction and search of parallel segment trees in an architecture independent way. Our proposed parallel algorithms are optimal in space and time compared to the corresponding sequential algorithms utilized to solve the introduced problems and are described in the context of the bulk-synchronous parallel (BSP) model of computation. Our methods are more scalable and can thus be made to work for larger values of processor size p relative to problem size n than other segment tree related algorithms that have been described on other realistic distributed-memory parallel models and also provide a natural way to approach searching problems on latency-tolerant models of computation that maintains a balanced query load among the processors.     

The one-to-one shortest-path problem: An empirical analysis with the two-tree Dijkstra algorithm

Four new shortest-path algorithms, two sequential and two parallel, for the source-to-sink shortest-path problem are presented and empirically compared with five algorithms previously discussed in the literature. The new algorithm, S22, combines the highly effective data structure of the S2 algorithm of Dial et al., with the idea of simultaneously building shortest-path trees from both source and sink nodes, and was found to be the fastest sequential shortest-path algorithm. The new parallel algorithm, PS22, is based on S22 and is the best of the parallel algorithms. We also present results for three new S22-type shortest-path heuristics. These heuristics find very good (often optimal) paths much faster than the best shortest-path algorithm.     

Projected subgradient algorithms on systems of equilibrium problems

The paper proposes two parallel and cyclic algorithms for solving systems of equilibrium problems in Hilbert spaces. The algorithms combine two methods including the diagonal subgradient method and the projection method with parallel or cyclic computations. The obtained results can be considered as improvements over several previously known methods for systems of equilibrium problems in computational steps. The algorithms have also allowed to reduce several assumptions imposed on bifunctions. The strongly convergent theorems are established under suitable conditions.     

Cognitive model exploration and optimization: a new challenge for computational science

Parameter space exploration is a common problem tackled on large-scale computational resources. The most common technique, a full combinatorial mesh, is robust but scales poorly to the computational demands of complex models with higher dimensional spaces. Such models are routinely found in the modeling and simulation community. To alleviate the computational requirements, I have implemented two parallelized intelligent search and exploration algorithms: one based on adaptive mesh refinement and the other on regression trees. These algorithms were chosen because there is a dual interest in approaches that allow searching a parameter space for optimal values, as well as exploring the overall space in general. Both intelligent algorithms reduce computational costs at some expense to the quality of results, yet the regression tree approach was orders of magnitude faster than the other methodologies.     

Enumeration of Pareto optimal multi-criteria spanning trees – a proof of the incorrectness of Zhou and Gen's proposed algorithm

The minimum spanning tree (MST) problem is a well-known optimization problem of major significance in operational research. In the multi-criteria MST (mc-MST) problem, the scalar edge weights of the MST problem are replaced by vectors, and the aim is to find the complete set of Pareto optimal minimum-weight spanning trees. This problem is NP-hard and so approximate methods must be used if one is to tackle it efficiently. In an article previously published in this journal, a genetic algorithm (GA) was put forward for the mc-MST. To evaluate the GA, the solution sets generated by it were compared with solution sets from a proposed (exponential time) algorithm for enumerating all Pareto optimal spanning trees. However, the proposed enumeration algorithm that was used is not correct for two reasons: (1) It does not guarantee that all Pareto optimal minimum-weight spanning trees are returned. (2) It does not guarantee that those trees that are returned are Pareto optimal. In this short paper we prove these two theorems.     

Parallel lightweight wavelet tree,suffix array and FM-index construction

We present parallel lightweight algorithms to construct wavelet trees, rank and select structures, and suffix arrays in a shared-memory setting. The work and depth of our first parallel wavelet tree algorithm match those of the best existing parallel algorithm while requiring asymptotically less memory and our second algorithm achieves the same asymptotic bounds for small alphabet sizes. Our experiments show that they are both faster and more memory-efficient than existing parallel algorithms. We also present an experimental evaluation of the parallel construction of rank and select structures, which are used in wavelet trees. Next, we design the first parallel suffix array algorithm based on induced copying. Our induced copying requires linear work and polylogarithmic depth for constant alphabets sizes. When combined with a parallel prefix doubling algorithm, it is more efficient in practice both in terms of running time and memory usage compared to existing parallel implementations. As an application, we combine our algorithms to build the FM-index in parallel.     

带重入的单台机排序问题

本文考虑带重入的单台机排序问题,重入是指每个工件在机器上加工不止一次.通过把重入模型转化为带平行链约束的排序问题,我们成功地获得了单机重入问题的两个目标函数的多项式时间最优算法,一个是总带权完工时间∑ωjCj,另一个是最大费用函数hmax.     

On consistency of recursive least squares identification algorithms for controlled auto-regression models

The recursive least squares (RLS) algorithms is a popular parameter estimation one. Its consistency has received much attention in the identification literature. This paper analyzes convergence of the RLS algorithms for controlled auto-regression models (CAR models), and gives the convergence theorems of the parameter estimation by the RLS algorithms, and derives the conditions that the parameter estimates consistently converge to the true parameters under noise time-varying variance and unbounded condition number. This relaxes the assumptions that the noise variance is constant and that high-order moments are existent. Finally, the proposed algorithms are tested with two example systems, including an experimental water-level system.     

Approximation algorithms for the bi-criteria weighted MAX-CUT problem

We consider a generalization of the classical MAX-CUT problem where two objective functions are simultaneously considered. We derive some theorems on the existence and the non-existence of feasible cuts that are at the same time near optimal for both criteria. Furthermore, two approximation algorithms with performance guarantee are presented. The first one is deterministic while the second one is randomized. A generalization of these results is given for the bi-criteria MAX-k-CUT problem.