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

c 2010 by Jonathan L. Gross

4 Chapter 13 Network Flows: Lec 16

Feasible Flows

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Section 13.1 Flows and Cuts in Networks 5

Fig 13.1.2

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6 Chapter 13 Network Flows: Lec 16

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Section 13.1 Flows and Cuts in Networks 7

Cuts in - Networks

Fig 13.1.3

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8 Chapter 13 Network Flows: Lec 16

Fig 13.1.4

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Section 13.1 Flows and Cuts in Networks 9

Fig 13.1.5

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10 Chapter 13 Network Flows: Lec 16

Relationship Between Flows and Cuts

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Section 13.1 Flows and Cuts in Networks 11

Fig 13.1.6

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12 Chapter 13 Network Flows: Lec 16

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Section 13.1 Flows and Cuts in Networks 13

Figure 13.1.7

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14 Chapter 13 Network Flows: Lec 16

c 2010 by Jonathan L. Gross

Section 13.1 Flows and Cuts in Networks 15

Max-Flow Problem and Min-Cut Problem

c 2010 by Jonathan L. Gross

16 Chapter 13 Network Flows: Lec 16

c 2010 by Jonathan L. Gross

Section 13.1 Flows and Cuts in Networks 17

Fig 13.1.8

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18 Chapter 13 Network Flows: Lec 16

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Section 13.2 Solving for Maximum-Flow 19

13.2 SOLVING FOR MAXIMUM-FLOW

Using Directed Paths to Augment Flow

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20 Chapter 13 Network Flows: Lec 16

Figure 13.2.1

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Section 13.2 Solving for Maximum-Flow 21

Figure 13.2.2

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22 Chapter 13 Network Flows: Lec 16

-Augmenting Paths

Fig 13.2.3

c 2010 by Jonathan L. Gross

Section 13.2 Solving for Maximum-Flow 23

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24 Chapter 13 Network Flows: Lec 16

Figure 13.2.4

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Section 13.2 Solving for Maximum-Flow 25

Figure 13.2.5

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26 Chapter 13 Network Flows: Lec 16

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Section 13.2 Solving for Maximum-Flow 27

Max-Flow Min-Cut Theorem

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28 Chapter 13 Network Flows: Lec 16

Algo 13.2.1:

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Section 13.2 Solving for Maximum-Flow 29

Finding an -Augmenting Path

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30 Chapter 13 Network Flows: Lec 16

Figure 13.2.7

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Section 13.2 Solving for Maximum-Flow 31

Algo 13.2.2:

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32 Chapter 13 Network Flows: Lec 16

Algo 13.2.3:

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Section 13.2 Solving for Maximum-Flow 33

Figure 13.2.8

Figure 13.2.9

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34 Chapter 13 Network Flows: Lec 16

Figure 13.2.10

Figure 13.2.11

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Section 13.5 Supplementary Exercises 35

Figure 13.2.12

13.5 SUPPLEMENTARY EXERCISES

c 2010 by Jonathan L. Gross