无回路网络中最短路问题的高效算法

无回路网络是一类重要的网络,给出在无回路网络中求解最短路树形图和任意顶点对间最短路的高效算法。该算法将顶点进行重新编号,结合广度优先探索法,从源顶点出发依次搜索每个顶点的所有出弧,并在弧的头部进行权值变换操作,可以得到最短路树形图和任意顶点对间最短路,算法复杂度分别为O(m)和O(m(n-m1/2))。该算法思想简便、复杂度低、易于操作。 关键词：     

计算两类网络的可靠性的多项式时间算法

定义了两类有向网络——ORC-网络和IRC-网络,并且提出一个计算它们的根通信可靠性(网络的一个特定结点(根点)能与其余每个结点通信的概率)的多项式时间算法.对于ORC-网络和IRC-网络,该算法的时间复杂度分别是O(｜E｜)和O(｜V｜·｜E｜),这里,｜V｜,｜E｜分别表示网络所含结点和边的数量.     

递归收缩算法中支点的处理策略研究

为了确保生成无向图割集的递归收缩算法的正确性和稳定性,对算法中种子顶点是支点的情形进行了分析,并采取了新的处理策略。分析了支点具有一个非可吸簇的情形,引进附加吸入的概念,修正了种子顶点的BFSO值取值规则,解决了现有算法可能遗漏割集的问题。针对支点没有非可吸簇的情形,给出了一个新的处理策略,解决了现有算法在某些特殊输入条件下效率不高的问题,在理论上分析了新处理策略的有效性,并做了相应的实验比较,理论分析和实验比较均表明：新的处理策略采用提高了递归收缩算法的稳定性。     

基于规则的最短路径查询算法

最短路径查询是图数据管理中非常重要的一类问题.研究了基于规则的最短路径查询,它是一类特殊的最短路径查询问题.给定起点和终点,基于规则的最短路径查询是指找到一条从起点到终点的最短路径,使得此路径经过用户指定点集中的所有点,并且某些点的访问顺序满足一定的偏序规则.该问题被证明是一个NP-hard问题.目前已有的工作侧重于空间数据集（两点之间的最短距离用欧氏距离表示）上基于规则的最短路径问题,它采用穷举的方式列出所有满足规则的路径,然后选择长度最小的路径作为问题的解.然而在实际的道路交通网中,两点之间的距离等于两点之间的最短路径的长度,它往往大于两点之间的欧氏距离;此外,采用穷举的方式会造成大量重复的计算.因此,设计了一种前向搜索算法以及一些优化技术来求解该问题.最后,在不同的真实数据集上设计了大量的实验来验证算法的有效性.实验结果表明,该算法可以快速给出问题的解,而且算法的效率在很大程度上超过了现有的算法.     

Superfaces: polygonal mesh simplification with bounded error

The algorithm presented simplifies polyhedral meshes within prespecified tolerances based on a bounded approximation criterion. The vertices in the simplified mesh are a proper subset of the original vertices. The algorithm, called Superfaces, makes two major contributions to the research in this area: it uses a bounded approximation approach, which guarantees that a simplified mesh approximates the original mesh to within a prespecified tolerance (that is, every vertex v in the original mesh will lie within a user specified distance ϵ of the simplified mesh); its face merging procedure is efficient and greedy-that is, it does not backtrack or undo any merging once completed and thus, the algorithm is practical for simplifying very large meshes     

An Efficient Algorithm for Finding All Hinge Vertices on Trapezoid Graphs

The distance between at least two vertices becomes longer after the removal of a hinge vertex. Thus a faulty hinge vertex will increase the overall communication cost in a network. Therefore, finding the set of all hinge vertices in a graph can be used to identify critical nodes in a real network. An O(n log n) time algorithm has been proposed here to find all hinge vertices of a trapezoid graph with n vertices.     

平面轮廓的螺旋填充轨迹生成算法

在快速成型和数控领域中对平面轮廓区域的填充是比较繁琐复杂的步骤。为充分扬弃顶点偏置和线段偏置的优缺点,提出了顶点线段混合偏置算法,即在凹点处采用线段偏置,而在凸点处则采用顶点偏置或插入线段方式;为优化起落刀次数,提出用对角曲线连接偏置曲线形成螺旋轨迹的算法,即在归类相同的相邻两条偏置曲线中,以顶点较多的作为主偏置曲线,利用K-D树在相邻多边形查找主偏置曲线每个顶点的最近点,依次求出对角曲线的离散点并且连接获得螺旋轨迹。     

Interrogating the structure of fuzzy cognitive maps

 Causal algebra in fuzzy cognitive maps (FCMs) plays a critical role in the analysis and design of FCMs. Improving causal algebra in FCMs to model complicated situations has been one of the major research topics in this area. In this paper we propose a dynamic causal algebra in FCMs which can improve FCMs' inference and representation capability. The dynamic causal algebra shows that the indirect, strongest, weakest and total effects a vertex influences another in the FCM not only depend on the weights along all directed paths between the two vertices but also the states of the vertices on the directed paths. Therefore, these effects are nonlinear dynamic processes determined by initial conditions and propagated in the FCM to reach a static or cyclic pattern. We test our theory with a simple example.     

A new formulation and approach for the black and white traveling salesman problem

This paper proposes a new formulation and a column generation approach for the black and white traveling salesman problem. This problem is an extension of the traveling salesman problem in which the vertex set is divided into black vertices and white vertices. The number of white vertices visited and the length of the path between two consecutive black vertices are constrained. The objective of this problem is to find the shortest Hamiltonian cycle that covers all vertices satisfying the cardinality and the length constraints. We present a new formulation for the undirected version of this problem, which is amenable to the Dantzig–Wolfe decomposition. The decomposed problem which is defined on a multigraph becomes the traveling salesman problem with an extra constraint set in which the variable set is the feasible paths between pairs of black vertices. In this paper, a column generation algorithm is designed to solve the linear programming relaxation of this problem. The resulting pricing subproblem is an elementary shortest path problem with resource constraints, and we employ acceleration strategies to solve this subproblem effectively. The linear programming relaxation bound is strengthened by a cutting plane procedure, and then column generation is embedded within a branch-and-bound algorithm to compute optimal integer solutions. The proposed algorithm is used to solve randomly generated instances with up to 80 vertices.     

Greedy rankings and arank numbers

A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices of the same rank contains a vertex of strictly larger rank. A ranking is locally minimal if reducing the rank of any single vertex produces a non-ranking. A ranking is globally minimal if reducing the ranks of any set of vertices produces a non-ranking. A ranking is greedy if, for some ordering of the vertices, it is the ranking produced by assigning ranks in that order, always selecting the smallest possible rank. We will show that these three notions are equivalent. If a ranking satisfies one property it satisfies all three. As a consequence of this and known results on arank numbers of paths we improve known upper bounds for on-line ranking of paths and cycles.     

An efficient network flow code for finding all minimum cost s–t cutsets

Cutset algorithms have been well documented in the operations research literature. A directed graph is used to model the network, where each node and arc has an associated cost to cut or remove it from the graph. The problem considered in this paper is to determine all minimum cost sets of nodes and/or arcs to cut so that no directed paths exist from a specified source node s to a specified sink node t. By solving the dual maximum flow problem, it is possible to construct a binary relation associated with an optimal maximum flow such that all minimum cost s–t cutsets are identified through the set of closures for this relation. The key to our implementation is the use of graph theoretic techniques to rapidly enumerate this set of closures. Computational results are presented to suggest the efficiency of our approach.Scope and purposeThis paper describes the technical details of a network flow algorithm used to find all minimum cost s–t cutsets in any network topology. The motivation for this work was to provide additional automated analysis capability to a military network targeting system. Specifically, the problem is to identify a minimum cost set of nodes and/or arcs that when removed from the network, will disconnect a selected pair of origin–destination nodes. Algorithms for solving this problem are well understood, with an active research thrust in both the operations research and computer science academic communities in developing more efficient algorithms for larger networks. The main contribution of this paper is in extending these algorithms to quickly find all minimum cost cutset solutions. The implementation described in this paper outperformed conventional methods by several orders of magnitude on networks having thousands of nodes and arcs, with empirical solution times that grew linearly with the network size. The results translate to a real-time cutset analysis capability to support military targeting applications.     

A heuristic technique for generating minimal path and cutsets of a general network

Reliability evaluation techniques employ a variety of tools for system modeling and calculation of reliability indices. Amongst the most popular tools are network-based algorithms founded on the concept of minimal paths and minimal cutsets. This paper presents a heuristic programming technique for deducing minimal paths of a network. In this technique, only minimal paths are immediately generated without explicitly determining whether or not a path is minimal. This technique has been implemented on a digital computer to generate a minimal path matrix, which is in turn utilized to generate minimal cutsets of the network. In terms of computational speed, the results obtained compare well with existing algorithms. The technique requires minimum memory storage and minimum user-defined data to represent the topology of a network and follows a modular design strategy. Use of the algorithm is illustrated by examples.     

A linear algorithm for the number of degree constrained subforests of a tree

Recent work of Farrell is concerned with determining the total number of ways in which one can cover the vertices of a tree T with vertex disjoint paths. Such path covers are spanning subforests in which each vertex is restricted to have degree at most two. If b: V(T)→N is a positive integer-valued function, then finding a b-matching is equivalent to finding a spanning subgraph in which the degree of each vertex v is at most b(v). A linear-time algorithm for determining the number of b-matching in a tree is presented.     

Strong Menger connectivity with conditional faults on the class of hypercube-like networks

In this paper, we study the Menger property on a class of hypercube-like networks. We show that in all n-dimensional hypercube-like networks with n−2 vertices removed, every pair of unremoved vertices u and v are connected by min{deg(u),deg(v)} vertex-disjoint paths, where deg(u) and deg(v) are the remaining degree of vertices u and v, respectively. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, all hypercube-like networks still have the strong Menger property, even if there are up to 2n−5 vertex faults.     

A convex polyhedron approach of constructing chemical potential diagrams for multicomponent systems

A new algorithm for constructing chemical potential diagrams has been developed with the aid of consideration based on computation geometry. Almost all procedures are based on the derivation of the intersection between the polyhedron in n-dimension space and the superplane with (n-1) dimensions. This consists of the geometrical consideration based on the graph theoretical features in terms of vertex, edge, and facet and of the numerical considerations for the beneath-beyond criterion and for obtaining vertices or edges. This generalization makes it easy to treat mixture phases and also to treat phase relations as a function of temperature or pressure.     

Finding the minimum vertex distance between two disjoint convex polygons in linear time

Let V = v₁, v₂, …, v_m and W = w₁, w₂, …, w_n be two linearly separable convex polygons whose vertices are specified by their cartesian coordinates in order. An algorithm with O(m + n) worst-case time complexity is described for finding the minimum euclidean distance between a vertex v₁ in V and a vertex w_j in W. It is also shown that the algorithm is optimal.     

随机图的点可区别V-全染色算法

图[G]的点可区别V-全染色就是相邻的边、顶点与其关联边必须染不同的颜色,同时要求所有顶点的色集合也不相同,所用的最少颜色数称为图[G]的点可区别V-全色数。根据点可区别V-全染色的约束规则,设计了一种启发式的点可区别V-全染色算法,该算法借助染色矩阵及色补集合逐步迭代交换,每次迭代交换后判断目标函数值,当目标函数值满足要求时染色成功。给出了算法的详细描述、算法分析和算法测试结果,对给定点数的图进行了点可区别V-全染色猜想的验证。实验结果表明,该算法有很好的执行效率并可以得到给定图的点可区别V-全色数,并且算法的时间复杂度不超过[O(n3)]。     

Finding the k Shortest Paths in Parallel

A concurrent-read exclusive-write PRAM algorithm is developed to find the k shortest paths between pairs of vertices in an edge-weighted directed graph. Repetitions of vertices along the paths are allowed. The algorithm computes an implicit representation of the k shortest paths to a given destination vertex from every vertex of a graph with n vertices and m edges, using O(m+nk log ² k) work and O( log^3k log ^*k+ log n( log log k+ log ^*n)) time, assuming that a shortest path tree rooted at the destination is pre-computed. The paths themselves can be extracted from the implicit representation in O( log k + log n) time, and O(n log n +L) work, where L is the total length of the output. Received July 2, 1997; revised June 18, 1998.     

任意拓扑结构网格模型自适应调整和光顺算法

在改进拉普拉斯算子的同时，吸取平均曲率法的优点，提出一种任意网格模型自适应调整和光顺算法．该算法通过沿法矢方向和在切平面上同时对网格顶点进行调整，保证了调整后模型不仅光顺，而且网格形状均匀；该算法还可以根据不同的精度自动地对网格调整进行控制，有效地保留了原始模型中的特征信息．应用实例表明，该算法可以保证在满足精度要求的条件下，得到更合理的三角网格模型．     

寻求简单多边形凸壳的线性时间算法

本文提出在线性时间内构造简单多边形顶点凸壳的两种算法。第一个算法的基本思想是利用一种技巧对多边形顶点进行筛选，使剩余顶点的角的大小排成递增序，然后用Graham扫描方法删去非凸壳顶点，最后得到多边形凸壳的顶点序列.第二个算法不断删去多边形的凹点及新产生的 凹点，最后得到凸壳顶点序列。这两种算法简单，易于实现，时间复杂性都是O（n)。