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图的限制性燃烧连通度

山东大学学报（理学版） 2024年第2期59卷 91-99,109页

作者：薛睿滢魏宗田翟美娟西安建筑科技大学理学院陕西西安710055

连通度是度量网络抗毁性的一个重要指标,从图燃烧的角度将该参数推广,提出图的限制性燃烧连通度概念。在给出若干基本图类的限制性燃烧连通度的基础上,用数学规划方法研究路的笛卡尔积图、蜘蛛图的限制性燃烧连通度计算问题。通过分析... 详细信息

连通度是度量网络抗毁性的一个重要指标,从图燃烧的角度将该参数推广,提出图的限制性燃烧连通度概念。在给出若干基本图类的限制性燃烧连通度的基础上,用数学规划方法研究路的笛卡尔积图、蜘蛛图的限制性燃烧连通度计算问题。通过分析限制性燃烧连通度与图结构的关系,阐明该参数在刻画网络抗毁性方面的优势。

关键词：图网络抗毁性限制性燃烧连通度笛卡尔积图蜘蛛图燃烧数

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基于赋权连通度优化的图重构

纯粹数学与应用数学 2024年第3期40卷 548-557页

作者：冯欣魏宗田姜淑艳西安建筑科技大学数学系陕西西安710055

提出赋权图的S−T颠覆策略和赋权连通度意义下的图重构概念.通过研究某些典型图类的基于赋权连通度优化的重构方法,构造赋权连通度达到最大或最小的赋权图,揭示了图的赋权连通度与权值的大小、赋权方式和图结构之间的关系.

关键词：颠覆策略赋权图 S−T重构赋权连通度优化

Reliability Analysis of Facility Systems Subject to Edge Failures: Based on the Uncapacitated Fixed-Charge Location Problem

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Open Journal of Discrete Mathematics 2011年第3期1卷 153-159页

作者： zongtian wei Huayong Xiao 不详

A facility system can be modeled by a connected graph in which the vertices represent entities such as suppliers, distribution centers or customers and the edges represent facilities such as the paths of goods or information. The efficiency, and hence the reliability, of a facility system is to a large degree adversely affected by the edge failures in the network. Such failures may be caused by various natural disasters or terrorist attacks. In this paper, we consider facility systems’ reliability analysis based on the classical uncapacitated fixed-charge location problem when subject to edge failures. For an existing facility system, we formulate two models based on deterministic case and stochastic case to measure the loss in efficiency due to edge failures and give computational results and reliability envelopes for a specific example.

关键词： Facility System Reliability Edge Failure Uncapacitated Fixed-Charge Location Problem

Reliable Facility Systems Design Subject to Edge Failures: Based on the Uncapacitated Fixed-Charge Location Problem

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American Journal of Operations Research 2014年第3期4卷 164-172页

作者： Yuangang Pan Yali Du zongtian wei Department of Applied Mathematics Northwestern Polytechnical University Xi’an China Department of Mathematics Xi’an University of Architecture and Technology Xi’an China

The reliability of facility location problem has aroused wide concern recently. Many researchers focus on reliable and robust facility systems design under component failures and have obtained promising performance. However, the target and reliability of a facility system are to a large degree adversely affected by the edge failures in the network, which remains a deep study. In this paper, we focus on facility systems’ reliability subject to edge failures. For a facility location system, we formulate two models based on classical uncapacitated fixed-charge location problem under deterministic and stochastic cases. For a specific example, location decisions and the comparison of reliability under different location models are given. Extensive experiments verify that significant improvements in reliability can be attained simply by increasing the amount of operating cost.

关键词： Facility System Reliability Edge Failure Uncapacitated Fixed-Charge Location Problem

Analysis of Facility Systems’ Reliability Subject to Edge Failures: Based on the p-Median Problem

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American Journal of Operations Research 2011年第4期1卷 277-283页

作者： zongtian wei Huayong Xiao Yuxi Quan 不详

We view a facility system as a kind of supply chain and model it as a connected graph in which the nodes represent suppliers, distribution centers or customers and the edges represent the paths of goods or information. The efficiency, and hence the reliability, of a facility system is to a large degree adversely affected by the edge failures in the network. In this paper, we consider facility systems' reliability analysis based on the classical p-median problem when subject to edge failures. We formulate two models based on deterministic case and stochastic case to measure the loss in efficiency due to edge failures and give computational results and reliability envelopes for a specific example.

关键词： Facility System Reliability Edge Failure p-Median Problem Operating Efficiency

Reliability Analysis of Systems Based on the UFLP under Facility Failure and Conditional Supply Cases

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Advances in Pure Mathematics 2012年第2期2卷 128-132页

作者： Min Wang zongtian wei Yun He Department of Mathematics Xi’an University of Architecture and Technology Xi’an China

The reliability of facility location problems has been received wide attention for several decades. Researchers formulate varied models to optimize the reliability of location decisions. But the most of such studies are not practical since the models are too ideal. In this paper, based on the classical uncapacitated fixed-charge location problem (UFLP) and some supply constraints from the reality, we distinguish deterministic facility failure and stochastic facility failure cases to formulate models to measure the reliability of a system. The computational results and reliability envelopes for a specific example are also given.

关键词： Reliability Analysis Facility Failure Supply Constraint Uncapacitated Fixed Charge Location Problem

Vertex-Neighbor-Scattering Number Of Trees

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Advances in Pure Mathematics 2011年第4期1卷 160-162页

作者： zongtian wei Yong Liu Anchan Mai 不详

A vertex subversion strategy of a graph G=(V,E) is a set of vertices S V(G) whose closed neighborhood is deleted from G . The survival subgraph is denoted by G/S . We call S a cut-strategy of G if G/S is disconnected, or is a clique, or is φ . The vertex-neighbor scattering number of G is defined to be VNS(G)=max{ω(G/S)-|S|} , where S is any cut-strategy of G , and ω(G/G) is the number of the components of G/S . It has been proved that the computing problem of this parameter is NP–complete, so we discuss the properties of vertex-neighbor-scattering number of trees in this paper.

关键词： Vertex-Neighbor-Scattering Number Tree Path Star Comet

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基于邻域连通度优化的图的N[S]-T重构

山东大学学报（理学版） 2023年第6期58卷 40-45,76页

作者：常乐魏宗田西安建筑科技大学理学院陕西西安710055

基于最优化的思想考虑一个被破坏的网络的邻域抗毁性恢复,提出图的邻域颠覆策略和重构的概念。研究了基于邻域连通度优化的图的重构问题,给出了两个完全图的笛卡尔积图关于最佳邻域颠覆策略下的最优重构方法和算法。

关键词：邻域颠覆策略重构最优重构完全图笛卡尔积图

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非负l^1图及其在谱聚类中的应用

计算机工程与应用 2011年第27期47卷 6-7,23页

作者：史加荣杨威魏宗田西安建筑科技大学理学院西安710055

信息图的构造对许多机器学习任务来说是至关重要的。基于稀疏表示理论,提出了一种有向非负l1图。在构造此图的过程中,先将每个样例表示成其他样例的非负线性组合,再通过求解l1最小化问题来同时获得近邻样例和对应的相似度。最后将基于非... 详细信息

信息图的构造对许多机器学习任务来说是至关重要的。基于稀疏表示理论,提出了一种有向非负l1图。在构造此图的过程中,先将每个样例表示成其他样例的非负线性组合,再通过求解l1最小化问题来同时获得近邻样例和对应的相似度。最后将基于非负l1图的谱聚类方法应用于手写字符的聚类问题。与基于l1图的谱聚类方法相比,所提方法具有较好的聚类性能和较低的计算复杂度。

关键词：非负l1图谱聚类 l1最小化手写字符聚类