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Flows in Networks2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载
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- L.R.Ford 著
- 出版社: Princeton University Press
- ISBN:
- 出版时间:1962
- 标注页数:194页
- 文件大小:48MB
- 文件页数:203页
- 主题词:
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图书目录
CHAPTER Ⅰ STATIC MAXIMAL FLOW1
Introduction1
1.Networks2
2.Flows in networks4
3.Notation9
4.Cuts10
5.Maximal flow11
6.Disconnecting sets and cuts14
7.Multiple sources and sinks15
8.The labeling method for solving maximal flow problems17
9.Lower bounds on arc flows22
10.Flows in undirected and mixed networks23
11.Node capacities and other extensions23
12.Linear programming and duality principles26
13.Maximal flow value as a function of two arc capacities30
References35
CHAPTER Ⅱ FEASIBILITY THEOREMS AND COMBINATORIAL APPLICATIONS36
Introduction36
1.A supply-demand theorem36
2.A symmetric supply-demand theorem42
3.Circulation theorem50
4.The K?nig-Egerváry and Menger graph theorems53
5.Construction of a maximal independent set of admissible cells55
6.A bottleneck assignment problem57
7.Unicursal graphs59
8.Dilworth's chain decomposition theorem for partially ordered sets61
9.Minimal number of individuals to meet a fixed schedule of tasks64
10.Set representatives67
11.The subgraph problem for directed graphs75
12.Matrices composed of 0's and 1's79
References91
CHAPTER Ⅲ MINIMAL COST FLOW PROBLEMS93
Introduction93
1.The Hitchcock problem95
2.The optimal assignment problem111
3.The general minimal cost flow problem113
4.Equivalence of Hitchcock and minimal cost flow problems127
5.A shortest chain algorithm130
6.The minimal cost supply-demand problem:non-negative directed cycle costs134
7.The warehousing problem137
8.The caterer problem140
9.Maximal dynamic flow142
10.Project cost curves151
11.Constructing minimal cost circulations162
References169
CHAPTER Ⅳ MULTI-TERMINAL MAXIMAL FLOWS173
Introduction173
1.Forests,trees,and spanning subtrees173
2.Realization conditions176
3.Equivalent networks177
4.Network synthesis187
References191
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