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1.
在局部凸拓扑线性空间中给出了含约束集值映射超有效解的连通性定理,当目标函数及约束映射为锥弧连通的集值映射时,其超有效解集是连通的.  相似文献   

2.
研究了带约束条件集值优化问题近似Henig有效解集的连通性.在实局部凸Hausdorff空间中,讨论了可行域为弧连通紧的,目标函数为C-弧连通的条件下,带约束条件集值优化问题近似Henig有效解集的存在性和连通性.并给出了带约束条件集值优化问题近似Henig有效解集的连通性定理.  相似文献   

3.
图的连通度、超连通性和限制连通度是度量互连网络容错性的重要参数 .该文考虑n维M bius立方体网络MQn,证明了它的点和边连通度都为n ,当n是任何正整数时它是超连通的 ,当n≠ 2时它是超边连通的 ,当n≥ 3时它的限制点连通度和当n≥ 2时的限制边连通度都为 2n- 2 .  相似文献   

4.
序列连通空间   总被引:6,自引:0,他引:6  
黄琴 《数学研究》2005,38(2):157-162
序列连通性具有许多相似于连通的性质.本文讨论了拓扑空间的序列连通性,并给出了序列连通空间的刻面及其性质.  相似文献   

5.
本文研究赋范线性空间中集值映射向量优化问题超有效解集的连通性问题.证明了目标映射为锥拟凸的向量优化问题的超有效解集是连通的.  相似文献   

6.
集值映射最优化问题的严有效解集的连通性及应用   总被引:7,自引:0,他引:7  
本文对集值映射最优化问题引入严有效解的概念.证明了当目标函数为锥类凸的集值映射时,其目标空间里的严有效点集是连通的;若目标函数为锥凸的集值映射时,其严有效解集也是连通的.作为应用,讨论了超有效解集的连通性.  相似文献   

7.
图G称为上连通的,若对每个最小割集C,G-C有孤立点,G称为超连通的,若对每个最小割集C,G-C恰有两个连通分支,且其中之一为弧立点,本文刻划了上连通和超连通三次点传递图。  相似文献   

8.
在研究多目标规划的有效解集的连通性时,许多文献通过将集合的有效点集表示为某个连通集上闭的点集映射的象集以得到结果.本文通过反例说明了连通集上闭的点集映射的象集未必是连通集,从而揭示了多目标规划有效解集连通性研究中存在的问题.据此,借助于点集映射的上半连续性,本文给出了集合的Pareto有效点集和Pareto弱有效点集的另一形式的连通性结果.  相似文献   

9.
在局部凸拓扑线性空间中给出了集值向量优化问题强有效解的连通性定理.该定理是在可行域为弧连通的条件下得到的.  相似文献   

10.
互连网络通常以有向图为模型,有向图的弧连通度是网络可靠性的一个重要参数.设D是一个有向图,δ(D)是最小度,弧连通度为λ(D),则λ(D)≤δ(D).当λ(D)=δ(D)时,称有向图D是极大弧连通的.本文给出了依赖团数的有向图极大弧连通的一些充分条件.  相似文献   

11.
互连网络的向量图模型   总被引:1,自引:0,他引:1  
n-超立方体、环网、k元n超立方体、Star网络、煎饼(pancake)网络、冒泡排序(bubble sort)网络、对换树的Cayley图、De Brujin图、Kautz图、Consecutive-d 有向图、循环图以及有向环图等已被广泛地应用做处理机或通信互连网络.这些网络的性能通常通过它们的度、直径、连通度、H...  相似文献   

12.
Motivated by the problem of designing large packet radio networks, we show that the Kautz and de Bruijn digraphs with in- and outdegree d have arc-chromatic index 2d. In order to do this, we introduce the concept of even 1-factorizations. An even 1-factor of a digraph is a spanning subgraph consisting of vertex disjoint loops and even cycles; an even 1-factorization is a partition of the arcs into even 1-factors. We prove that if a digraph admits an even 1-factorization, then so does its line digraph. (In fact, we show that the line digraph admits an even 1-factorization even under a weaker assumption discussed below.) As a consequence, we derive the above property of the Kautz and de Bruijn digraphs relevant to packet radio networks. © 1993 John Wiley & Sons, Inc.  相似文献   

13.
In this paper, novel multi-layer networks with superior couplings are proposed firstly which are established on a non-strongly connected digraph. Within the multi-layer networks, a nonlinear coupling based on white noises is introduced, which is the feature of superior couplings. We adopt aperiodically adaptive intermittent pinning control to stabilize the multi-layer networks. An concrete analysis framework about selecting the target vertex of the control is revealed. Aperiodically adaptive intermittent control is employed on the vertex systems of the first layer networks, to achieve the stabilization of the first layer networks, where the couplings of drift terms are treated as negative effects on stabilization. With the help of noise stabilization, the stabilization of the other layers networks is realized based on the stability of the first layer networks and the characteristics of the superior coupling that is based on white noises. By employing graph theory and the Lyapunov method, an almost sure exponential stabilization criterion of the multi-layer networks is acquired. As a subsequent result, the proposed theory is applied to a class of stochastic coupled oscillators with sufficient conditions being given to ensure their stability. Finally, a numerical example is provided to illustrate the feasibility of the stated theoretical results.  相似文献   

14.
Boolean networks have been used as models of gene regulation and other biological networks. One key element in these models is the update schedule, which indicates the order in which states have to be updated. In Aracena et al. (2009) [1], the authors define equivalence classes that relate deterministic update schedules that yield the same update digraph and thus the same dynamical behavior of the network. In this paper we study algorithmical and combinatorial aspects of update digraphs. We show a polynomial characterization of these digraphs, which enables us to characterize the corresponding equivalence classes. We prove that the update digraphs are exactly the projections, on the respective subgraphs, of a complete update digraph with the same number of vertices. Finally, the exact number of complete update digraphs is determined, which provides upper and lower bounds on the number of equivalence classes.  相似文献   

15.
Boolean networks have been used as models of gene regulation and other biological networks, as well as for other kinds of distributed dynamical systems. One key element in these models is the update schedule, which indicates the order in which states have to be updated. In Salinas (2008) [22] and Aracena et al. (2009) [1], equivalence classes of deterministic update schedules according to the labeled digraph associated to a Boolean network (update digraph) were defined and it was proved that two schedules in the same class yield the same dynamical behavior. In this paper, we study the relations between the update digraphs and the preservation of limit cycles of Boolean networks iterated under non-equivalent update schedules. We show that the related problems lie in the class of NP-hard problems and we prove that the information provided by the update digraphs is not sufficient to determine whether two Boolean networks share limit cycles or not. Besides, we exhibit a polynomial algorithm that works as a necessary condition for two Boolean networks to share limit cycles. Finally, we construct some update schedule classes whose elements share a given limit cycle under certain conditions on the frozen nodes of it.  相似文献   

16.
Network design problems arise in a wide range of applied areas including telecommunications, computer networks, and transportation. In this paper, we address the following discrete capacitated multi-terminal network design problem. Given a connected digraph G = (V,A), a set of L potential facilities to be installed on each arc, and a set of K multi-terminal (non-simultaneous) commodity flow requirements, the problem is to find a set of facilities to install in order to route the K nonsimultaneous flows while minimizing the total fixed plus variable costs. We describe an exact procedure for solving this problem based on Benders decomposition. Our algorithm includes several features that significantly improve the efficiency of the basic approach. Computational results attest to the efficacy of the proposed algorithm, which can solve medium- to large-scale problems to optimality.  相似文献   

17.
Graph searching games involve a team of searchers that aims at capturing a fugitive in a graph. These games have been widely studied for their relationships with tree-and path-decomposition of graphs. In order to define decompositions for directed graphs, similar games have been proposed in directed graphs. In this paper, we consider such a game that has been defined and studied in the context of routing reconfiguration problems in WDM networks. Namely, in the processing game, the fugitive is invisible, arbitrary fast, it moves in the opposite direction of the arcs of a digraph, but only as long as it has access to a strongly connected component free of searchers. We prove that the processing game is monotone which leads to its equivalence with a new digraph decomposition.  相似文献   

18.
The concept of returnability is proposed for complex directed networks (digraphs). It can be seen as a generalization of the concept of reciprocity. Two measures of the returnability are introduced. We establish closed formulas for the calculation of the returnability measures, which are also related to the digraph spectrum. The two measures are calculated for simple examples of digraphs as well as for real-world complex directed networks and are compared with the reciprocity.  相似文献   

19.
In this paper we consider systems of transport and diffusion problems on one-dimensional domains coupled through transmission type boundary conditions at the endpoints and determine what types of such problems can be identified with respective problems on metric graphs. For the transport problem the answer is provided by a reformulation of a graph theoretic result characterizing line digraphs of a digraph, whereas in the case of diffusion the answer is provided by an algebraic characterization of matrices which are adjacency matrices of line graphs, which complements known results from graph theory and is particularly suitable for this application.  相似文献   

20.
A digraph D is supereulerian if D has a spanning eulerian subdigraph. BangJensen and Thomass′e conjectured that if the arc-strong connectivity λ(D) of a digraph D is not less than the independence number α(D), then D is supereulerian. In this paper, we prove that if D is an extended cycle, an extended hamiltonian digraph, an arc-locally semicomplete digraph, an extended arc-locally semicomplete digraph, an extension of two kinds of eulerian digraph, a hypo-semicomplete digraph or an extended hypo-semicomplete digraph satisfyingλ(D) ≥α(D), then D is supereulerian.  相似文献   

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