Graphenalgorithmen cd
description
Transcript of Graphenalgorithmen cd
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Albert-Ludwigs-Universität Freiburg
Michael Hummel & Martin Ebner
Freiburg, den 02.07.13
Kruskal, Dijkstra, Huffman & Co
Graphenalgorithmen
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Kruskal‘s Algorithmus
7
5
8
7
5
9
11
8
15
6
9
A C
B
E
G
D
F
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Kruskal‘s Algorithmus
7
5
8
7
5
9
11
8
15
6
9
A C
B
E
G
D
F
A C
B
E
G
D
F
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Kruskal‘s Algorithmus
7
5
8
7
5
9
11
8
15
6
A C
B
E
G
D
F
A C
B
E
G
D
F
9
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Kruskal‘s Algorithmus
7
5
8
7
5
9
11
8
15
6
9
A C
B
E
G
D
F
A C
B
E
G
D
F
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Kruskal‘s Algorithmus
7
5
8
7
5
9
11
8
15
6
9
A C
B
E
G
D
F
A C
B
E
G
D
F
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Kruskal‘s Algorithmus
7
5
8
7
5
9
11
8
15
6
9
A C
B
E
G
D
F
A C
B
E
G
D
F
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Kruskal‘s Algorithmus
7
5
8
7
5
9
11
8
15
6
9
A C
B
E
G
D
F
A C
B
E
G
D
F
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Kruskal‘s Algorithmus
7
5
8
7
5
9
11
8
15
6
9
A C
B
E
G
D
F
A C
B
E
G
D
F
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Kruskal‘s Algorithmus
7
5
8
7
5
9
11
8
15
6
9
A C
B
E
G
D
F
A C
B
E
G
D
F
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Kruskal‘s Algorithmus
7
5
8
7
5
9
11
8
15
6
9
A C
B
E
G
D
F
A C
B
E
G
D
F
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Kruskal‘s Algorithmus
7
5
8
7
5
9
11
8
15
6
9
A C
B
E
G
D
F
A C
B
E
G
D
F
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Dijkstra‘s Algorithmus
U
14 15
2 11
9 10
69
70 ∞
∞
∞∞
∞
𝑆 = {𝑈}A
B
C
D
E
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Dijkstra‘s Algorithmus
U
14 15
2 11
9 10
69
70 7
∞
∞
9
𝑆 = {𝑈}
14
A
B
C
D
E
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Dijkstra‘s Algorithmus
U
14 15
2 11
9 10
69
70 7
∞
9
𝑆 = {𝑈, 𝐸}
22
A
B
C
D
E
14
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Dijkstra‘s Algorithmus
U
14 15
2 11
9 10
69
70 7
∞
9
𝑆 = {𝑈, 𝐸, 𝐶}
11
A
B
C
D
E
20
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Dijkstra‘s Algorithmus
U
14 15
2 11
9 10
69
70 7
9
𝑆 = {𝑈, 𝐸, 𝐶, 𝐵}
11 20
20A
B
C
D
E
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Dijkstra‘s Algorithmus
U
14 15
2 11
9 10
69
70 7
9
𝑆 = {𝑈, 𝐸, 𝐶, 𝐵, 𝐴}
11
A
B
C
D
E
20
20
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Dijkstra‘s Algorithmus
U
14 15
2 11
9 10
69
70 7
9
𝑆 = 𝑈, 𝐸, 𝐶, 𝐵, 𝐴, 𝐷
11
A
B
C
D
E
20
20
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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U.S &
Kanada
Europa
Afrika
Asien &
Pazifik& Karibik
Lateinamerika
4‘972 343
40
11
1‘345
2‘721
5
2‘946
Bandwidth 2011
[Gbps]
Internet
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Telegeography Research
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Gewurzelte Bäume
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Veit Bach
†1619
Lips
† 1620
Johann
† 1626
Johann
1604 – 73
Heinrich
1615 – 92
Christoph
1613 – 61
Wendel
1619 – 82
Jacob
1655 – 1718
Joh. Ludwig
1677 – 1731
Nikolaus Ephraim
1690 – 1760
Georg Michael
1701 – 77
Johann Christian
1743 – 1814
Johann Ambrosius
1645 – 95
Georg Christoph
1624 – 97
Johann Christoph
1645 – 93
Johann Sebastian
1685 – 1750
Wilhelm Friedemann
1710 – 84
Carl Phillip Emanuel
1714 – 88
Johann Gottfried Bernhard
1715 – 39
Johann Christoph Friedrich
1732 – 95
Johann Christian
1732 – 95
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Binärbäume
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Johann Wolfgang von
Goethe
Johann Caspar
Goethe
Friedrich Georg
Göthe
Cornelia
Walther
Hans Christian
Göthe
Sibylla
Werner
Hans Göthe
Sibylla Werner
Johannes Werner
Frieda Kuner
Georg
Walther
Anna M.
Streng
Jacob Walther
Barbara Dürr
Andreas Streng
Margarethe Auel
Catharina Elisabeth
Textor
Johann Wolfgang
Textor
Anna Magaretha
Lindheimer
Christoph H.
Textor
Maria C.
Appel
Cornelius
Lindheimer
Catharina E.
Seip
Johann Textor
Anna M. Priester
Johann Appel
Anna Maria Walter
Johann Lindheimer
Anna Windecker
Johann v. Pettenhausen
Elisabeth Streuber
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Huffman‘s Algorithmus
MISSISSIPPI
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Huffman‘s Algorithmus
MISSISSIPPI
Zeichen M P I S
Häufigkeit 1 2 4 4
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Huffman‘s Algorithmus
MISSISSIPPI
Zeichen M P I S
Häufigkeit 1 2 4 4
1M
2P
4I
4S
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Huffman‘s Algorithmus
1M
2P
4I
4S
3
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Huffman‘s Algorithmus
1M
2P
4I
4S
3
7
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Huffman‘s Algorithmus
1M
2P
4I
4S
3
711
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Huffman‘s Algorithmus
1M
2P
4I
4S
3
7
0
0 1
1
110 1
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Huffman‘s Algorithmus
1M
2P
4I
4S
3
7110
0
0 1
1
1
Zeichen M P I S
Häufigkeit 1 2 4 4
Huffman 000 001 01 1
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Huffman‘s Algorithmus
MISSISSIPPI =
000 01 1 1 01 1 1 01 001 001 01
(21 Bit)
Zeichen M P I S
Häufigkeit 1 2 4 4
Huffman 000 001 01 1
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Huffman‘s Algorithmus
MISSISSIPPI =
01001101010010010101001101010010100100
10101001101010011010010010101000001010
00001001001
(88 Bit)
Zeichen M P I S
Häufigkeit 1 2 4 4
ASCII 01001101 01010000 01001001 01010011
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
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Huffman‘s Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
0,00% 2,00% 4,00% 6,00% 8,00% 10,00% 12,00% 14,00% 16,00% 18,00%
E
N
I
S
R
A
T
D
H
U
L
C
G
M
O
B
W
F
K
Z
P
V
ß
J
Y
X
QWikipedia
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ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor
invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et
accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est
Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam
nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At
vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata
sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr,
sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam
voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no
sea takimata sanctus est Lorem ipsum dolor sit amet. Duis autem vel eum iriure dolor in hendrerit
in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla facilisis at vero eros et
accumsan et iusto odio dignissim qui blandit praesent luptatum zzril delenit augue duis dolore te
feugait nulla facilisi. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy
nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim
veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo
consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat,
vel illum dolore eu feugiat nulla facilisis at vero eros et accumsan et iusto odio dignissim qui blandit
praesent luptatum zzril delenit augue duis dolore te feugait nulla facilisi. Nam liber tempor cum
soluta nobis eleifend option congue nihil imperdiet doming id quod mazim placerat facer possim
assum. Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod
tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud
exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel
eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat
nulla facilisis. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren,
no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur
sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat,
sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd
gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet,
consetetur sadipscing elitr, At accusam aliquyam diam diam dolore dolores duo eirmod eos erat, et
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Huffman‘s Algorithmus
1L
1T
3
4E
2
590
0 1
1
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
2S 1
2
0
1K
011 110 101 100 001 010 0
0 1
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Kruskal‘s Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
4
4
3
3
2
3
2
4
4
4
A B
E
F
I
D
G
5
H
2
3
4
J
3
4
3
C
2
4
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Kruskal‘s Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
4
4
3
3
2
3
2
4
4
4
A B
E
F
I
D
G
5
H
2
3
4
J
3
4
3
C
2
4
A B
E
F
I
D
G
H
J
C
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Kruskal‘s Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
A B
E
F
I
D
G
H
4
4
3
3
2
3
2
4
4
4
A B
E
F
I
D
G
5
H
2
3
4
J
3
4
3
C
2
4
J
C
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A*-Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Freiburgℎ = 290
Karlsruheℎ = 200
Ulmℎ = 140
Stuttgartℎ = 160
Heilbronnℎ = 140
Nürnbergℎ = 0
Augsburgℎ = 120
135
200
85
95170
210
145
85
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A*-Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Freiburg
Karlsruhef = 135 + 200
Ulmf = 200 + 140
Stuttgartℎ = 160
Heilbronnℎ = 140
Nürnbergℎ = 0
Augsburgℎ = 120
135
200
85
95170
210
145
85
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A*-Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Freiburg
Karlsruhef = 335
Ulmf = 340
Stuttgartℎ = 160
Heilbronnℎ = 140
Nürnbergℎ = 0
Augsburgℎ = 120
135
200
85
95170
210
145
85
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A*-Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Freiburg
Karlsruhe
Ulmf = 340
Stuttgartf = 135 + 85 + 160
Heilbronnf = 135 + 95 + 140
Nürnbergℎ = 0
Augsburgℎ = 120
135
200
85
95170
210
145
85
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A*-Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Freiburg
Karlsruhe
Ulmf = 340
Stuttgartf = 380
Heilbronnf = 370
Nürnbergℎ = 0
Augsburgℎ = 120
135
200
85
95170
210
145
85
![Page 47: Graphenalgorithmen cd](https://reader035.fdocuments.net/reader035/viewer/2022081404/55874050d8b42a56388b46ae/html5/thumbnails/47.jpg)
A*-Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Freiburg
Karlsruhe
Ulm
Stuttgartf = 380
Heilbronnf = 370
Nürnbergℎ = 0
Augsburgf = 200 + 85 + 120
135
200
85
95170
210
145
85
![Page 48: Graphenalgorithmen cd](https://reader035.fdocuments.net/reader035/viewer/2022081404/55874050d8b42a56388b46ae/html5/thumbnails/48.jpg)
A*-Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Freiburg
Karlsruhe
Ulm
Stuttgartf = 380
Heilbronnf = 370
Nürnbergℎ = 0
Augsburgf = 405
135
200
85
95170
210
145
85
![Page 49: Graphenalgorithmen cd](https://reader035.fdocuments.net/reader035/viewer/2022081404/55874050d8b42a56388b46ae/html5/thumbnails/49.jpg)
A*-Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Freiburg
Karlsruhe
Ulm
Stuttgartf = 380
Heilbronn Nürnbergf = 135 + 95 + 170
Augsburgf = 405
135
200
85
95170
210
145
85
![Page 50: Graphenalgorithmen cd](https://reader035.fdocuments.net/reader035/viewer/2022081404/55874050d8b42a56388b46ae/html5/thumbnails/50.jpg)
A*-Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Freiburg
Karlsruhe
Ulm
Stuttgartf = 380
Heilbronn Nürnbergf = 400
Augsburgf = 405
135
200
85
95170
210
145
85
![Page 51: Graphenalgorithmen cd](https://reader035.fdocuments.net/reader035/viewer/2022081404/55874050d8b42a56388b46ae/html5/thumbnails/51.jpg)
A*-Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Freiburg
Karlsruhe
Ulm
Stuttgart
Heilbronn Nürnbergf = 400 < 430
Augsburgf = 405
135
200
85
95170
210
145
85
![Page 52: Graphenalgorithmen cd](https://reader035.fdocuments.net/reader035/viewer/2022081404/55874050d8b42a56388b46ae/html5/thumbnails/52.jpg)
A*-Algorithmus
02.07.2013 Graphenalgorithmen Michael Hummel & Martin Ebner
Freiburg
Karlsruhe
Ulm
Stuttgart
Heilbronn Nürnberg400km
Augsburgf = 405
135
200
85
95170
210
145
85
![Page 53: Graphenalgorithmen cd](https://reader035.fdocuments.net/reader035/viewer/2022081404/55874050d8b42a56388b46ae/html5/thumbnails/53.jpg)
A*-Algorithmus
Stuttgart
Heilbronn
Nürnberg
Augsburg
Ulm
Freiburg
Karlsruhe
![Page 54: Graphenalgorithmen cd](https://reader035.fdocuments.net/reader035/viewer/2022081404/55874050d8b42a56388b46ae/html5/thumbnails/54.jpg)
A*-Algorithmus
![Page 55: Graphenalgorithmen cd](https://reader035.fdocuments.net/reader035/viewer/2022081404/55874050d8b42a56388b46ae/html5/thumbnails/55.jpg)
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