chapter 13cs4203/files/gt-lec16.pdfchapter 13 netw or k flo ws: lec 16 13.1 flo ws and cuts in netw...

Chapter 13Network Flows: Lec 16

13.1 Flows and Cuts in Networks13.2 Solving the Maximum-Flow Problem

1 c 2010 by Jonathan L. Gross

2 Chapter 13 Network Flows: Lec 16

13.1 FLOWS AND CUTS IN NETWORKS

c 2010 by Jonathan L. Gross

Section 13.1 Flows and Cuts in Networks 3

Figure 13.1.1



Feasible Flows



Fig 13.1.2



Cuts in - Networks

Fig 13.1.3



Fig 13.1.4



Fig 13.1.5



Relationship Between Flows and Cuts



Fig 13.1.6



Figure 13.1.7



Max-Flow Problem and Min-Cut Problem



Fig 13.1.8


Section 13.2 Solving for Maximum-Flow 19

13.2 SOLVING FOR MAXIMUM-FLOW

Using Directed Paths to Augment Flow



Figure 13.2.1



Figure 13.2.2



-Augmenting Paths

Fig 13.2.3



Figure 13.2.4



Figure 13.2.5



Max-Flow Min-Cut Theorem



Algo 13.2.1:



Finding an -Augmenting Path



Figure 13.2.7



Algo 13.2.2:



Algo 13.2.3:



Figure 13.2.8

Figure 13.2.9



Figure 13.2.10

Figure 13.2.11


Section 13.5 Supplementary Exercises 35

Figure 13.2.12

13.5 SUPPLEMENTARY EXERCISES


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