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《Systems Engineering》 1997-01
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The Two -Way How -Augmenting Algorithm for Solving the Minimum Flow Problem of a Network

Ning Xuanxi  
Blockage is a kind of phenomenon t happened grequently in a transport network in which human beings are the moving subjects. The minimum flow defined in this paper means the maximal flow through a network in the most seriously-blocked situation of the network. It is an important parameter in designing a transport network, especially an emergency evaluation network. In this paper the fundamental concepts of minimum flow of a network are introduced on the basis of blocking flow theory, and the minimum flow problem is defined from the viewpoint of combined optimization. An efficient algorithm called " Two way Flow -Augmenting Method " is developed to solve the minimum flow problem and demonstrated by the example in detail.
【Fund】: 国家自然科学基金资助项目 课题号79470044
【CateGory Index】: O221;O157.5
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【References】
Chinese Journal Full-text Database 10 Hits
1 WU Wei-wei,NING Xuan-xi (College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China);Sensitivity Analysis on the Minimum Saturated Flow of Blocking Networks[J];Systems Engineering;2006-08
2 WANG Ji(Wuhan Science Technology University,Wuhan,Hubei,430070);A Solution of the Fuzzy Network Minimal Flow Problem[J];Journal of Guangdong Radio & Television University;2006-04
3 LI Xin-hua1 ZHANG Zhao-ning2 HOU Rui1 1.Flight Service Center,Southwest Air Traffic Management Bureau of CAAC,Chengdu 610202,China 2.Air Traffic Management Department, Civil Aviation University of China,Tianjin 300300,China;Research of the Structural Stability of the Route Network System[J];Journal of Transportation Engineering and Information;2009-01
4 Ning Xuanxi Industry and Business College,Nanjing University of Aeronautics & Astronautics Nanjing,210016;Tower Graph——A Kind of Extended Hamiltonian Graph[J];Journal of Nanjing University of Aeronautics & Astronautics;2000-05
5 Wu Weiwei1,Ning Xuanxi2(1.College of Civil Aviation,Nanjing University of Aeronautics & Astronautics,Nanjing,210016,China;2.College of Economics and Management,Nanjing University of Aeronautics & Astronautics,Nanjing,210016,China);Minimum Saturated Flow Problem in Directed Network and Its Algorithm[J];Journal of Nanjing University of Aeronautics & Astronautics;2007-05
6 Ning Xuanxi (College of Industry and Business,NUAA Nanjing,210016);Graph Simplex Algorithm for Solving Minimal Flow Problem of a Network[J];JOURNAL OF NANJING UNIVERSITY OF AERONAUTICS & ASTRONAUTICS;1997-05
7 WU Wei-wei and NING Xuan-xi(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,Jiangsu,China);A Monte-Carlo simulation approach for stochastic flow of emergency evacuation networks based on different forward directed augmented paths[J];Journal of Shandong University(Natural Science);2006-06
8 Ning Xuanxi Qian Lei Sun Yu College of Economics and Management,Nanjing University of Aeronautics & Astronautics Nanjing 210016,P.R.China;Research on Stochastic Flow in a Transportation Network by Simulational Method[J];Journal of Data Acquisition & Processing;2002-03
9 WU Wei-wei,NING Xuan-xi(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing Jiangsu 210016,China);Solve of the Minimum Saturated Flow in the Transportation Network[J];Mathematics in Practice and Theory;2006-09
10 WANG Ji,ZHOU Shu-min(Science College,Wuhan University of Technology,Wuhan 430070,China);A Global Optimization Method for Minimum-CostSaturated Flow Problem[J];Journal of Shantou University(Natural Science Edition);2007-04
【Citations】
Chinese Journal Full-text Database 2 Hits
1 Ning Xuanxi;A Branch -and -Bound Method for the Minimal Flow Problem of a Directed Network[J];Systems Engineering;1996-05
2 Ning Xuanxi (College of Industry and Business, NUAA Nanjing,210016);Graph Simplex Method for Solution of Maximum Flow Problem in a Network[J];TRANSACTIONS OF NANJING UNIVERSITY OF AERONAUTICS & ASTRONAUTICS;1996-05
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 WU Wei-wei,NING Xuan-xi (College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China);Sensitivity Analysis on the Minimum Saturated Flow of Blocking Networks[J];Systems Engineering;2006-08
2 WANG Ji(Wuhan Science Technology University,Wuhan,Hubei,430070);A Solution of the Fuzzy Network Minimal Flow Problem[J];Journal of Guangdong Radio & Television University;2006-04
3 LI Xin-hua1 ZHANG Zhao-ning2 HOU Rui1 1.Flight Service Center,Southwest Air Traffic Management Bureau of CAAC,Chengdu 610202,China 2.Air Traffic Management Department, Civil Aviation University of China,Tianjin 300300,China;Research of the Structural Stability of the Route Network System[J];Journal of Transportation Engineering and Information;2009-01
4 Ning Xuanxi Industry and Business College,Nanjing University of Aeronautics & Astronautics Nanjing,210016;Tower Graph——A Kind of Extended Hamiltonian Graph[J];Journal of Nanjing University of Aeronautics & Astronautics;2000-05
5 NING Xuan-xi, NING Angelika (College of Economics and Management, Nanjing University of Aeronautics & Astrounautics,Nanjing, 210016,China);Research on Knight′s Circuit Problem in Generalized Chessboards and Their Solutions[J];Journal of Nanjing University of Aeronautics & Astronautics;2004-03
6 Wu Weiwei1,Ning Xuanxi2(1.College of Civil Aviation,Nanjing University of Aeronautics & Astronautics,Nanjing,210016,China;2.College of Economics and Management,Nanjing University of Aeronautics & Astronautics,Nanjing,210016,China);Minimum Saturated Flow Problem in Directed Network and Its Algorithm[J];Journal of Nanjing University of Aeronautics & Astronautics;2007-05
7 Ning Xuanxi (College of Industry and Business,NUAA Nanjing,210016);Graph Simplex Algorithm for Solving Minimal Flow Problem of a Network[J];JOURNAL OF NANJING UNIVERSITY OF AERONAUTICS & ASTRONAUTICS;1997-05
8 WU Wei-wei and NING Xuan-xi(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,Jiangsu,China);A Monte-Carlo simulation approach for stochastic flow of emergency evacuation networks based on different forward directed augmented paths[J];Journal of Shandong University(Natural Science);2006-06
9 Ning Xuanxi Qian Lei Sun Yu College of Economics and Management,Nanjing University of Aeronautics & Astronautics Nanjing 210016,P.R.China;Research on Stochastic Flow in a Transportation Network by Simulational Method[J];Journal of Data Acquisition & Processing;2002-03
10 LI Hong-bo,ZHAN Ji-zan(College of Mathematics and Information Science,Yantai Normal University,Yantai 264025,China);Practical design and dynamic implementation of efficient algorithms for max-flow problem[J];Computer Engineering and Design;2006-22
【Co-references】
Chinese Journal Full-text Database 10 Hits
1 CHEN Chun-mei, REN Fu-tian, RONG Jian, HE Yu-long ( Transportation Research Center, Beijing Polytechnic University, Beijing 100022, China );Research on Development of Capacity of Road Network[J];Journal of Beijing Polytechnic University;2002-02
2 CHEN Chun-mei, REN Fu-tian, RONG Jian, TANG Hui( 1. Beijing Municipal Institute of City Planning and Design, Beijing 100045, China;2. Research Center of Transportation Engineering, Beijing Polytechnic University, Beijing 100022, China );Application of Random Effective Theory to the Study of the Capacity of Road Network[J];Journal of Beijing Polytechnic University;2002-04
3 ZHU Xiao yan, SUN Wei, TANG Shui yuan (School of Mechanical Engineering and Automation, Beijing Institute of Technology, Beijing100081);Supply-System Oriented Virtual Enterprises[J];JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY;2000-04
4 WANG Fang,HOU Chao-zhen(Department of Automatic Control, School of Information Science and Technology, Beijing Institute of Technology, Beijing100081, China);Evaluation of the Reliability of Stochastic Flow Network Using Monte Carlo Method and the Petri Net[J];Journal of Beijing Institute of Technology;2004-07
5 WANG Fang, HOU Chao-zhen (School of Information Science and Technology, Beijing Institute of Technology, Beijing100081, China);New Algorithm to Evaluate the Unreliability of Flow Networks Based on Minimal Cutsets[J];北京理工大学学报(英文版);2004-01
6 ZHANG Guang-ming,NING Xuan-xi,MENG Han-qing;The Principles and Ways of Improving Shipyard Material Supply Management[J];Commercial Research;2001-03
7 HU Zhcng-hua (College of Economics & Management, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China);An Evaluation of E-business from a Business Process[J];Commercial Research;2003-01
8 HU Zheng-hua, NING Xuan-xi (College of Management, Nanjing University of Aero & Astro, Nanjing 210016, China);Service Chain Concept, Model and Application[J];Commercial Research;2003-07
9 Ma Yufang et al;Comparison and Analysis of Enterprise Group, Supply Chain and Fictitious Enterprise[J];Auto Industry Research;2001-02
10 HU Zheng hua 1,XU Le ping 2,GU Xue hua 3 (1.College of Economics & Management, Nanjing Univ. of Aeronautics & Astronautics, Nanjing 210016,China; 2.Marine Eng. College,Dalian Maritime Univ.,Dalian 116026,China; 3 Dalian Maritime Safety Adminis;Ship maintenance management system based on modern communication technology[J];Journal of Dalian Maritime University;2002-01
【Secondary References】
Chinese Journal Full-text Database 10 Hits
1 WU Wei-wei,NING Xuan-xi (College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China);Sensitivity Analysis on the Minimum Saturated Flow of Blocking Networks[J];Systems Engineering;2006-08
2 LI Xin-hua1 ZHANG Zhao-ning2 HOU Rui1 1.Flight Service Center,Southwest Air Traffic Management Bureau of CAAC,Chengdu 610202,China 2.Air Traffic Management Department, Civil Aviation University of China,Tianjin 300300,China;Research of the Structural Stability of the Route Network System[J];Journal of Transportation Engineering and Information;2009-01
3 Ning Xuanxi Industry and Business College,Nanjing University of Aeronautics & Astronautics Nanjing,210016;Tower Graph——A Kind of Extended Hamiltonian Graph[J];Journal of Nanjing University of Aeronautics & Astronautics;2000-05
4 Wu Weiwei1,Ning Xuanxi2(1.College of Civil Aviation,Nanjing University of Aeronautics & Astronautics,Nanjing,210016,China;2.College of Economics and Management,Nanjing University of Aeronautics & Astronautics,Nanjing,210016,China);Minimum Saturated Flow Problem in Directed Network and Its Algorithm[J];Journal of Nanjing University of Aeronautics & Astronautics;2007-05
5 Ning Xuanxi (College of Industry and Business,NUAA Nanjing,210016);Graph Simplex Algorithm for Solving Minimal Flow Problem of a Network[J];JOURNAL OF NANJING UNIVERSITY OF AERONAUTICS & ASTRONAUTICS;1997-05
6 WU Wei-wei and NING Xuan-xi(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,Jiangsu,China);A Monte-Carlo simulation approach for stochastic flow of emergency evacuation networks based on different forward directed augmented paths[J];Journal of Shandong University(Natural Science);2006-06
7 Ning Xuanxi Qian Lei Sun Yu College of Economics and Management,Nanjing University of Aeronautics & Astronautics Nanjing 210016,P.R.China;Research on Stochastic Flow in a Transportation Network by Simulational Method[J];Journal of Data Acquisition & Processing;2002-03
8 WU Wei-wei,NING Xuan-xi(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing Jiangsu 210016,China);Solve of the Minimum Saturated Flow in the Transportation Network[J];Mathematics in Practice and Theory;2006-09
9 WANG Ji,ZHOU Shu-min(Science College,Wuhan University of Technology,Wuhan 430070,China);A Global Optimization Method for Minimum-CostSaturated Flow Problem[J];Journal of Shantou University(Natural Science Edition);2007-04
10 WU Wei-wei~1,NING Xuan-xi~2 (1.Civil Aviation College,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;2.College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China);Evaluation of the reconstructing scheme making streets one-way[J];Systems Engineering-Theory & Practice;2009-07
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