Data base

1
???????
????

• ??? 2002/11/11
• Data base
• Label Setting Algorithm
• Label Correcting Algorithm

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Data Base
3
From To Distance
1 2 6
1 4 3
1 5 2
2 3 2
2 5 2
2 6 1
3 6 3
4 5 1
5 2 3
5 6 5
6
2
1
2
3
2
1
3
2
3
3
4
5
6
1
5
?30???
4
To Distance
2 6
4 3
5 2
3 2
5 2
6 1
6 3
5 1
2 3
6 5
Forward star
(1)Point 1
(2)Point 4
6
2
(3)Point 7
1
2
3
(4)Point 8
2
1
3
2
3
3
(5)Point 9
4
5
6
1
5
?25???
5
Label Setting Algorithm
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Dijkstras Shortest-Path Algorithm(Label Setting
Algorithm )

• ??????K??,?????????
• s t,?? s?t?????
• Step1
• ????d(x)??s??x????
• (x????????)
• when
• when
• ??ys

7

• Step2
• ?
• a(y,x)??y?x????,?y???????x??, a(y,x)???
• Ex
• a(s,x)a(x,t)10 , a(s,t)a(x,s)a(t,x)???
• ?d(x)???????x (?s????y)?y
• Ex
• d(s)0 , d(a)5 , d(b)7 , d(c)6 , ya

8

• Step3
• ?yt?,???s?t?????
• ??????Step2

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????

• ??????,????????????,??????P(x)????x????P(x)????
• Ex
• P(a)s , P(b)a , P(t)b

t
s
b
a
10
??

• ?????

3
2
4
7
2
2
3
3
11
ys
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d(s)0
d(1)mind(1) , d(s) a(s,1)min8,044
d(2)mind(2) , d(s) a(s,2)min8,077
d(3)mind(3) , d(s) a(s,3)min8,033
d(4)8
d(t)8
y3
S?3?????3
13
d(s)0
d(1)4
d(2)7
d(3)3(???y)
d(4)mind(4) , d(3) a(3,4)min8,336
d(t)8
y1
S?1?????4
14
d(s)0
d(1)4(???y)
d(2)mind(2) , d(1) a(1,2)min7,437
d(3)3(???y)
d(4)6
d(t)8
y4
S?4?????6
15
d(s)0
d(1)4(???y)
d(2)7
d(3)3(???y)
d(4)6(???y)
d(t) mind(t) , d(4) a(4,t)min8,628
y2
S?2?????7
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d(s)0
d(1)4(???y)
d(2)7(???y)
d(3)3(???y)
d(4)6(???y)
d(t) mind(t) , d(2) a(2,t)min8,728
y8
S?t?????8
17
Label Correcting Algorithm
18
Label Correcting AlgorithmFord(1946) ,
Moore(1957) , Bellman(1958)

• ??????n?,??s
• ???s?k???x???
• ?k??, ???
• ?????,?k?????(??)??
• k??,?????????
• S?????????????

???
??
??
??
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K

• ???K?????????,???????????,????????
• Ex

2
1
3
???node 1 ?node 3 ?????,?node 3?K?2
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Algorithm

• ????
• k0 , d(s)0 , when
• Ss , kk1 , go to Step1

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• Step1
• -???S???????????d(x)
• -d(x)mind(x),d(s)a(s,x)
• Step2
• -S j d(j) ?step1???
• -T(j)S????j?????
• Step3
• when klt(n-1) , kk1 , go to
  Step1
• when klt(n-1) , Stop
• when kn , Stop

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??
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k j T(j) d(x) k update Distanc Label S
0 d(1)0 L0,8, 8, 8 1
1 2,4 2 1 d(2)min8,011 1 Y
4 1 d(4)min8,044 1 Y L0,1, 8,4 2,4
P0,1,0,1
2 3 3 2 d(3)min8,112 2 Y L0,1,2,4 3
P0,1,2,1
3 4 4 3 d(4)min4,213 3 Y L0,1,2,3 4
P0,1,2,3
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??

• ?forward star?????????data base
• ?label setting ? label correcting Algorithm
• ???1????????

3
2
1
3
1
4
9
5
7
7
3
4
6
10
9
6
5
7
4
7
5
8
6
9
3
2
5
8