Illustration of the TSP algorithm docx

1
Illustration of the TSP algorithm
  
  
  

 
 

 



2
Key idea
 !
""#"
"!$!
"%&''(')!*+

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
% 
#
3
,!(-
.
,!(-'&&)'''(('
-"&&/+!(&'-!()/&'''
')
.

0+!(1,1!2'!()/&-&'
)
333
.
'((+4,'&-'+/-5*)
2')-'&!+/)'
.
'+))(()'4
6
)'('(&)&'-'&)''(((&)&'-
6 &'-)')')''(5
6 (')''(')&'-+5
6 )()))-''5
6 ))-''
6
%2')'(+
6 ) 3333
4
Application to convolutional code
')& ,%
)''(
' )& )&$'  
!'+'2')
78' 9 78' 9 
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)⊕'
)⊕'
,0:%;%:4'&2')<)'&)&2')8)5)9
'&')859 8)⊕'5)⊕'9
5
Use encoder state space (Trellis Diagram)

&(+
)




=

=

0    


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6

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=

=


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
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
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



=

=






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
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')& 
)''( 

 
 



!
7
Viterbi Decoder action
,0:%;%:4

'&2')<)'&
)&2')8)5)9'&')859 8)⊕'5
)⊕'9
>?/(&)4'&8)5)9>@
7!!(+85A)5)9 7!8)⊕'5)⊕'A)5)9 
 7!8'5'9
'B'&-2(

8
%')7'&
.
%40
&')
5
&

5'C'-&')
!*''+*)&2')
.
-&)'('()&4
?-&')5
&


=(('!''!2(5
&
'

5'2')
*(*C'-*-
.
0'/'*')')*+&-''-)'('(
)&-'&')
C*5-')&)'!'(+@&'&&')

9
Convolutional Codes 9
%')7'('(&8)'D&9

.
'('()&('
05C'-&')!*''+)&2')
)'&C'-&')!*'(("@)&2')
'&''@)&2')
.
0''@2')'C'-*-&-(("
@''&-*(("@(
'
10
%')74(('
.
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&
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.
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&
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11
7:#;:4
)(')&&:-'!+3333333333333
*!'-+''!

')&&)''(5


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!
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5')')''(+!(!3
)&&)''(*/E'5'

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!
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
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!
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
/E'&
F)&*(&'=:)
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8989&'&!+
%
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8*-9
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13
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.
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14
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.
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.
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 '&? -
&')'')'
4
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$%
H
$%
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0')&2')*-0
&


0*)&2')*-H5
)&2')*-5I
15
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.
0'!!(+
&'&!!(+
&)&())&
2')*'
'&
.
#*)&*&7*
7!!(+
.

0!'&'
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 
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))p1(p(4(
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16
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.
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17
0)''('-F)'('()&4/ $B+('
(>+,!&)&'-4'(
J
8'!&'9
18
Markov model example
Figure from Huang et al, via
19
Markov Model
.
What is the probability of 5 consecutive up
days?
.
Sequence is up-up-up-up-up
I.e., state sequence is 1-1-1-1-1
. P(1,1,1,1,1) =

π










 >8H9

 H
20
Application to Hidden Markov Models
%''4
0C
'

5)*))&*!!(+
&!'
'''--'&!+!!(
)((&
''!!(

')(')
!'
)'!-'&5
))&'-)&!!(+&!'
'(+)5'!('>'(!
'&KK&&'LL&M')'

C&&'/&(
N7?77?0;4))-'''&+'
21
HMM
 





H



789
78&*'9  
78'")'-9







H


 '(!!(+

H



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
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''>

22
Calculate
Probability ( observation | model )
0((4



789
78&*'9 

78'")'-9







H

O
H


7!!(+5757575PPP


O
PP
PP
OPP
PP
OPP
PHP OPHP
PP
HPP
H

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
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''>

H
&&!!(Q