绘制统筹网络图的一个标号算法及应用

本文给出了一个绘制统筹网络图的有效算法，称之为标号算法．利用标号算法可使计算机在只接收到各工序间紧前紧后关系的数据后，便可生成网络优化中必需的网络图形．利用该算法我们还建立了网络优化计算机辅助设计系统，该方法和计算机辅助设计系统，目前已在山东省兴隆庄煤矿井下的拆除和安装工程中得到了具体应用，收到了良好的效果．     

AT-free图的配对控制集算法

本文给出了配对控制集在AT-free图的BFS-树上分布的结构性质．利用这些性质，我们给出了求解AT-free图类最小配对控制集的多项式时间算法．     

图的独立数的一个新下界

设α（Ｇ）表示简单图Ｇ＝（Ｖ，Ｅ）的独立数．本文给出了α（Ｇ）的一个新的下界：α（Ｇ）≥∑ｖ∈Ｖ（λｄ（ｖ）＋１）／（ｄ（ｖ）＋λｄ（ｖ）＋１），其中λｄ（ｖ）＝ｍａｘ｛０，βＮ（ｖ）－ｄ（ｖ）｝，ｄ（ｖ）＝｜Ｎ（ｖ）｜，Ｎ（ｖ）＝｛ｗ∈Ｖ｜（ｖ，ｗ）∈Ｅ｝，βＮ（ｖ）＝ｍｉｎｗ∈Ｎ（ｖ）ｄ（ｗ）．     

序数权重统一表示下的权重稳健性Hasse图分析

认识多种序数赋权方法的共性,有助于摆脱方法选择困扰,增强其实用效果。首先以线性函数为目标函数,以权重关系构造约束条件,建立线性规划。在此基础上证明了任意权重均可由线性规划的极值点集来表示,揭示了序数权重实质上是极值点的加权线性组合。进一步针对赋权方法稳健性不足的问题,利用极值点构建偏序关系,通过Hasse图增强权重排序的稳健性。实例分析表明,尽管序数权重不同,但与偏序方法相结合,均能得到类似的分析结果。     

一个在置换图中寻找DFS树的最优算法

本是通过在连通置换图中构造辅助树的方法,给出了一个在具有n个顶点的置换图G中寻找深度优先支撑树（简称,DFS树）的最优算法,并证明了该算法的时间复杂性为O(n)。     

群的一个Domain结构

群可以通过在其上赋予循环群拓扑构造群的Domain模型，从而实现群的可计算性。群上的循环群偏序集及其对偶都是连续的偏序集，这个连续偏序集是代数Domain的充分必要条件是群的单位元是代数元。如果在pseudo-有限的群G及其循环群偏序集的对偶￡^op[G]上分别赋予循环群拓扑和Scott拓扑，那么恒同函数是连续的。     

Hamilton连通图的一个充分条件

Let G be a3-connected graph with n vertices.The paper proves that if for each pair of verti-ces u and v of G,d(u,v)=2,has|N(u)∩N(v)|≤α（αis the minimum independent set num-ber),and then max{d(u),d(v)|≥n 1/2,then G is a Hamilton connected graph.     

一种扩展的影响图及其求解方法

针对影响图在实际应用中的参数建模困难问题,提出了一种扩展的影响图.引入credal集作为影响图的概率参数,以表达专家的不精确和不完整信度,集成多来源的定性和定量信息.引入credal集后,影响图的推理难度进一步加大.提出了将其转化为credal网络求解的思路,并给出了一种基于路径选择的求解算法.最后用一个实例验证了算法的有效性.     

Banach空间上一个定理的推广

针对Banach空间上一个定理,指出其命题条件过强,并在减弱后的条件下,运用Zorn引理给出证明,从而对该定理进行了推广.     

偏序集最小顶点割算法与最小费用赶工问题

在网络计划问题中,一项大的工程由许多工序合成。工序与工序之间存在着一定的前后关系,每个工序有着自己的正常加工时间和通过赶工所能达到的最短加工时间以及每赶工一天的赶工费用。设一项工程的正常工期为T天,通过对所有可能的工序赶工,整个工程能达到的最短工期为S天。本文的问题是,对于任意给定的t(S t相似文献   

A project game for PERT networks

An important topic in PERT networks is how to allocate the total expedition (or delay) for situations in which the project is not executed as planned. In order to do that we define a TU project game that satisfies some desirable properties from the management project and game theory point of view.     

An Optimal Algorithm to Find the Jump Number of Partially Ordered Sets

The jump number of a partially ordered set (poset) P isthe minimum number of incomparable adjacent pairs (jumps) in some linearextension of P. The problem of finding a linear extension of Pwith minimum number of jumps (jump number problem) is known to beNP-hard in general and, at the best of our knowledge, no exactalgorithm for general posets has been developed. In this paper, wegive examples of applications of this problem and propose for thegeneral case a new heuristic algorithm and an exactalgorithm. Performances of both algorithms are experimentallyevaluated on a set of randomly generated test problems.     

求有限集合覆盖的构造方法

在近似算法领域,集合覆盖问题是研究的比较早和比较透彻的问题之一.文中解决与经典SCP不同的另一问题,针对有限集合覆盖的构造,提出一种构造有限集合上的集合覆盖的算法,并且给出了该算法的完备性证明.该算法简单有效,是一种用于构造集合覆盖的规范方法.     

An Algorithm for the Generalized Assignment Problem with Special Ordered Sets

The generalized assignment problem (GAP), the 0–1 integer programming (IP) problem of assigning a set of n items to a set of m knapsacks, where each item must be assigned to exactly one knapsack and there are constraints on the availability of resources for item assignment, has been further generalized recently to include cases where items may be shared by a pair of adjacent knapsacks. This problem is termed the generalized assignment problem with special ordered sets of type 2 (GAPS2). For reasonably large values of m and n the NP-hard combinatorial problem GAPS2 becomes intractable for standard IP software, hence there is a need for the development of heuristic algorithms to solve such problems. It will be shown how a heuristic algorithm developed previously for the GAP problem can be modified and extended to solve GAPS2. Encouraging results, in terms of speed and accuracy, have been achieved.     

Meir-Keeler Type Contractions for Tripled Fixed Points

In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.     

对换网络和乘积循环网络的超连通性

本文证明了对换网络和乘积循环网络是超连通的。     

Due Date-Based Metrics for Activity Importance in Stochastic Activity Networks

A metric pair for assessing the importance of activities in stochastic activity networks based on completing a project on time (or reaching other project milestones) is presented. The metric pair is recommended as a supplement to other metrics of activity importance that have been suggested for use with Monte Carlo simulation. The differences in behavior of the various metrics are analyzed to help understand the additional types of insights that would be available by including the new metrics in simulation-based analyses.     

WDM网络中的一个改进的最优半光通道路由算法

本文在一个限定的条件下，提出了一个WDM网络中的寻找最优半光通道算法，使时间复杂度从O（k^2n km knlog(kn))提高到O（k^2n km nlogn)。     

Height Preserving Minimal Interval Extensions

We consider minimal interval extensions of a partial order which preserve the height of each vertex. We show that minimal interval extensions having this property bijectively correspond to the maximal chains of a sublattice of the lattice of maximal antichains of the given order. We show that they also correspond to the set of minimal interval extensions of a certain extension of this order.