scholarly journals Chance distribution of the maximum flow of uncertain random network

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Yuhong Sheng ◽  
Jinwu Gao
Keyword(s):  
Random Network ◽  
Maximum Flow ◽  
Chance Distribution ◽  
Distribution Of The Maximum ◽  
Uncertain Random Network

The maximum flow problem of uncertain random network

2017 ◽  
Vol 8 (5) ◽  
pp. 667-675 ◽  
Author(s):  
Gang Shi ◽  
Yuhong Sheng ◽  
Dan A. Ralescu
Keyword(s):  
Flow Problem ◽  
Random Network ◽  
Maximum Flow ◽  
Maximum Flow Problem ◽  
Uncertain Random Network

Entropy of Uncertain Random Variables wi h Application to Minimum Spanning Tree Problem

2017 ◽  
Vol 25 (04) ◽  
pp. 497-514 ◽  
Author(s):  
Yuhong Sheng ◽  
Gang Shi ◽  
Dan A. Ralescu
Keyword(s):  
Relative Entropy ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Random Network ◽  
Random Variables ◽  
Distribution Functions ◽  
Chance Distribution ◽  
Uncertain Random Network ◽  
Minimum Spanning Tree Problem ◽  
The Difference

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicted. Based on the notion of chance measure, a concept of uncertain random entropy is introduced and used to provide a quantitative measurement of the uncertainty associated with uncertain random variables and its properties are studied in this paper. Relative entropy is a measure of the difference between two distribution functions. In order to deal with the divergence of uncertain random variables via chance distributions, this paper proposes also the relative entropy for uncertain random variables, as well as it investigates some mathematical properties of this concept. As an application, a model is presented to formulate a minimum spanning tree problem with uncertain random edge weights involving a relative entropy chance distribution. Finally, a numerical example of an uncertain random network is put forward to illustrate the effectiveness of the proposed model.

scholarly journals Adaptation of Random Binomial Graphs for Testing Network Flow Problems Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1716
Author(s):  
Adrian Marius Deaconu ◽  
Delia Spridon
Keyword(s):  
Network Flow ◽  
Large Scale ◽  
Random Network ◽  
Minimum Cost ◽  
Maximum Flow ◽  
Network Flow Problems ◽  
Commodity Flow ◽  
Vast Number ◽  
Flow Problems ◽  
Execution Speed

Algorithms for network flow problems, such as maximum flow, minimum cost flow, and multi-commodity flow problems, are continuously developed and improved, and so, random network generators become indispensable to simulate the functionality and to test the correctness and the execution speed of these algorithms. For this purpose, in this paper, the well-known Erdős–Rényi model is adapted to generate random flow (transportation) networks. The developed algorithm is fast and based on the natural property of the flow that can be decomposed into directed elementary s-t paths and cycles. So, the proposed algorithm can be used to quickly build a vast number of networks as well as large-scale networks especially designed for s-t flows.

scholarly journals A SOLUTION ALGORITHM FOR p-MEDIAN LOCATION PROBLEM ON UNCERTAIN RANDOM NETWORKS

2020 ◽  
Vol 35 (1) ◽  
pp. 055
Author(s):  
Akram Soltanpour ◽  
Fahimeh Baroughi ◽  
Behrooz Alizadeh
Keyword(s):  
Optimization Model ◽  
Location Problem ◽  
Random Network ◽  
Solution Algorithm ◽  
Random Networks ◽  
Median Problem ◽  
Chance Theory ◽  
Numerical Example ◽  
Model Based ◽  
Uncertain Random Network

This paper investigatesthe classical $p$-median location problem in a network in which some of the vertex weights and the distances between vertices are uncertain and while others are random. For solving the $p$-median problem in an uncertain random network, an optimization model based on the chance theory is proposed first and then an algorithm is presented to find the $p$-median. Finally, a numerical example is given to illustrate the efficiency of the proposed method

The Minimum Cost Flow Problem of Uncertain Random Network

2018 ◽  
Vol 35 (03) ◽  
pp. 1850016
Author(s):  
Soheila Abdi ◽  
Fahimeh Baroughi ◽  
Behrooz Alizadeh
Keyword(s):  
Flow Model ◽  
Flow Problem ◽  
Random Network ◽  
Minimum Cost ◽  
Random Variable ◽  
Minimum Cost Flow ◽  
Feasible Set ◽  
Uncertain Random Network ◽  
Minimum Cost Flow Problem ◽  
Cost Flow

The aim of this paper is to present a novel method for solving the minimum cost flow problem on networks with uncertain-random capacities and costs. The objective function of this problem is an uncertain random variable and the constraints of the problem do not make a deterministic feasible set. Under the framework of uncertain random programming, a corresponding [Formula: see text]-minimum cost flow model with a prespecified confidence level [Formula: see text], is formulated and its main properties are analyzed. It is proven that there exists an equivalence relationship between this model and the classical deterministic minimum cost flow model. Then an algorithm is proposed to find the maximum amount of [Formula: see text] such that for it, the feasible set of [Formula: see text]-minimum cost flow model is nonempty. Finally, a numerical example is presented to illustrate the efficiency of our proposed method.

Minimum spanning tree problem of uncertain random network

2014 ◽  
Vol 28 (3) ◽  
pp. 565-574 ◽  
Author(s):  
Yuhong Sheng ◽  
Zhongfeng Qin ◽  
Gang Shi
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Random Network ◽  
Uncertain Random Network ◽  
Minimum Spanning Tree Problem

scholarly journals Network Robustness Analysis Based on Maximum Flow

2021 ◽  
Vol 9 ◽  
Author(s):  
Meng Cai ◽  
Jiaqi Liu ◽  
Ying Cui
Keyword(s):  
Structural Integrity ◽  
Random Network ◽  
Robustness Analysis ◽  
Maximum Flow ◽  
Indicator System ◽  
Average Degree ◽  
Network Robustness ◽  
Damage Rate ◽  
Flow Capacity ◽  
Critical Damage

Network robustness is the ability of a network to maintain a certain level of structural integrity and its original functions after being attacked, and it is the key to whether the damaged network can continue to operate normally. We define two types of robustness evaluation indicators based on network maximum flow: flow capacity robustness, which assesses the ability of the network to resist attack, and flow recovery robustness, which assesses the ability to rebuild the network after an attack on the network. To verify the effectiveness of the robustness indicators proposed in this study, we simulate four typical networks and analyze their robustness, and the results show that a high-density random network is stronger than a low-density network in terms of connectivity and resilience; the growth rate parameter of scale-free network does not have a significant impact on robustness changes in most cases; the greater the average degree of a regular network, the greater the robustness; the robustness of small-world network increases with the increase in the average degree. In addition, there is a critical damage rate (when the node damage rate is less than this critical value, the damaged nodes and edges can almost be completely recovered) when examining flow recovery robustness, and the critical damage rate is around 20%. Flow capacity robustness and flow recovery robustness enrich the network structure indicator system and more comprehensively describe the structural stability of real networks.

Application of Lattice Imaging Techniques to Amorphous Films

1975 ◽  
Vol 33 ◽  
pp. 8-9
Author(s):  
S. R. Herd ◽  
P. Chaudhari
Keyword(s):  
Nearest Neighbor ◽  
Random Network ◽  
Imaging Techniques ◽  
Network Models ◽  
Accurate Method ◽  
Direct Transmission ◽  
Lattice Imaging ◽  
Transmission Electron ◽  
Lattice Planes ◽  
Nearest Neighbor Distances

Electron diffraction and direct transmission have been used extensively to study the local atomic arrangement in amorphous solids and in particular Ge. Nearest neighbor distances had been calculated from E.D. profiles and the results have been interpreted in terms of the microcrystalline or the random network models. Direct transmission electron microscopy appears the most direct and accurate method to resolve this issue since the spacial resolution of the better instruments are of the order of 3Å. In particular the tilted beam interference method is used regularly to show fringes corresponding to 1.5 to 3Å lattice planes in crystals as resolution tests.

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