chapter 13cs4203/files/gt-lec16.pdfchapter 13 netw or k flo ws: lec 16 13.1 flo ws and cuts in netw...
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![Page 1: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/1.jpg)
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
![Page 2: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/2.jpg)
2 Chapter 13 Network Flows: Lec 16
13.1 FLOWS AND CUTS IN NETWORKS
c 2010 by Jonathan L. Gross
![Page 3: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/3.jpg)
Section 13.1 Flows and Cuts in Networks 3
Figure 13.1.1
c 2010 by Jonathan L. Gross
![Page 4: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/4.jpg)
4 Chapter 13 Network Flows: Lec 16
Feasible Flows
c 2010 by Jonathan L. Gross
![Page 5: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/5.jpg)
Section 13.1 Flows and Cuts in Networks 5
Fig 13.1.2
c 2010 by Jonathan L. Gross
![Page 6: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/6.jpg)
6 Chapter 13 Network Flows: Lec 16
c 2010 by Jonathan L. Gross
![Page 7: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/7.jpg)
Section 13.1 Flows and Cuts in Networks 7
Cuts in - Networks
Fig 13.1.3
c 2010 by Jonathan L. Gross
![Page 8: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/8.jpg)
8 Chapter 13 Network Flows: Lec 16
Fig 13.1.4
c 2010 by Jonathan L. Gross
![Page 9: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/9.jpg)
Section 13.1 Flows and Cuts in Networks 9
Fig 13.1.5
c 2010 by Jonathan L. Gross
![Page 10: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/10.jpg)
10 Chapter 13 Network Flows: Lec 16
Relationship Between Flows and Cuts
c 2010 by Jonathan L. Gross
![Page 11: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/11.jpg)
Section 13.1 Flows and Cuts in Networks 11
Fig 13.1.6
c 2010 by Jonathan L. Gross
![Page 12: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/12.jpg)
12 Chapter 13 Network Flows: Lec 16
c 2010 by Jonathan L. Gross
![Page 13: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/13.jpg)
Section 13.1 Flows and Cuts in Networks 13
Figure 13.1.7
c 2010 by Jonathan L. Gross
![Page 14: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/14.jpg)
14 Chapter 13 Network Flows: Lec 16
c 2010 by Jonathan L. Gross
![Page 15: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/15.jpg)
Section 13.1 Flows and Cuts in Networks 15
Max-Flow Problem and Min-Cut Problem
c 2010 by Jonathan L. Gross
![Page 16: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/16.jpg)
16 Chapter 13 Network Flows: Lec 16
c 2010 by Jonathan L. Gross
![Page 17: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/17.jpg)
Section 13.1 Flows and Cuts in Networks 17
Fig 13.1.8
c 2010 by Jonathan L. Gross
![Page 18: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/18.jpg)
18 Chapter 13 Network Flows: Lec 16
c 2010 by Jonathan L. Gross
![Page 19: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/19.jpg)
Section 13.2 Solving for Maximum-Flow 19
13.2 SOLVING FOR MAXIMUM-FLOW
Using Directed Paths to Augment Flow
c 2010 by Jonathan L. Gross
![Page 20: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/20.jpg)
20 Chapter 13 Network Flows: Lec 16
Figure 13.2.1
c 2010 by Jonathan L. Gross
![Page 21: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/21.jpg)
Section 13.2 Solving for Maximum-Flow 21
Figure 13.2.2
c 2010 by Jonathan L. Gross
![Page 22: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/22.jpg)
22 Chapter 13 Network Flows: Lec 16
-Augmenting Paths
Fig 13.2.3
c 2010 by Jonathan L. Gross
![Page 23: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/23.jpg)
Section 13.2 Solving for Maximum-Flow 23
c 2010 by Jonathan L. Gross
![Page 24: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/24.jpg)
24 Chapter 13 Network Flows: Lec 16
Figure 13.2.4
c 2010 by Jonathan L. Gross
![Page 25: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/25.jpg)
Section 13.2 Solving for Maximum-Flow 25
Figure 13.2.5
c 2010 by Jonathan L. Gross
![Page 26: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/26.jpg)
26 Chapter 13 Network Flows: Lec 16
c 2010 by Jonathan L. Gross
![Page 27: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/27.jpg)
Section 13.2 Solving for Maximum-Flow 27
Max-Flow Min-Cut Theorem
c 2010 by Jonathan L. Gross
![Page 28: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/28.jpg)
28 Chapter 13 Network Flows: Lec 16
Algo 13.2.1:
c 2010 by Jonathan L. Gross
![Page 29: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/29.jpg)
Section 13.2 Solving for Maximum-Flow 29
Finding an -Augmenting Path
c 2010 by Jonathan L. Gross
![Page 30: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/30.jpg)
30 Chapter 13 Network Flows: Lec 16
Figure 13.2.7
c 2010 by Jonathan L. Gross
![Page 31: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/31.jpg)
Section 13.2 Solving for Maximum-Flow 31
Algo 13.2.2:
c 2010 by Jonathan L. Gross
![Page 32: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/32.jpg)
32 Chapter 13 Network Flows: Lec 16
Algo 13.2.3:
c 2010 by Jonathan L. Gross
![Page 33: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/33.jpg)
Section 13.2 Solving for Maximum-Flow 33
Figure 13.2.8
Figure 13.2.9
c 2010 by Jonathan L. Gross
![Page 34: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/34.jpg)
34 Chapter 13 Network Flows: Lec 16
Figure 13.2.10
Figure 13.2.11
c 2010 by Jonathan L. Gross
![Page 35: Chapter 13cs4203/files/GT-Lec16.pdfChapter 13 Netw or k Flo ws: Lec 16 13.1 Flo ws and Cuts in Netw orks 13.2 Solving the Maxim um-Flo w P ro b lem 1 c 2010 b y Jonathan L. Gross](https://reader033.vdocument.in/reader033/viewer/2022052004/60174a0ac662c564112b0aef/html5/thumbnails/35.jpg)
Section 13.5 Supplementary Exercises 35
Figure 13.2.12
13.5 SUPPLEMENTARY EXERCISES
c 2010 by Jonathan L. Gross