CHINESE POSTMAN ALGORITHM

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CHINESE POSTMAN ALGORITHM
This is used when we are trying to find the
shortest route round a network such all the arcs
are travelled along at least once.
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Step 1 Identify all the odd vertices
Step 2 Form all possible pairings of odd
vertices
Step 3 For each pairing find the arcs that make
the total distance of repeats as small as
possible
Step 4 Choose the pairing with the smallest sum
and add this to the graph
Step 5 Find a route that works and add the
smallest sum found in Step 4 to the sum of
all the weights in the original graph to
find the length of the required route.
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Add this to the network
A postman starts at the depot T and has to
deliver mail along all the streets shown in the
network below. Find a route that means he
travels the shortest possible distance.
Odd vertices are B, G, H T
Possible pairings
The shortest extra route is
Possible route is
BG HT
TABEAGHEGHFDFECDTCBCT
Route BEG HECT
You dont believe me?
Length 1.7 1.8 3.5
BH GT
Want to see it?
Route BEH GECT
Length 1.5 2.0 3.5
BT GH
Route BCT GH
Length 0.8 0.9 1.7
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T
Total length of all original paths is 16.45 km
D
A
B
C
Add on the extra routes BCT and GH 1.7 km
E
F
Shortest length 16.45 1.7 18.15 km
G
H
Route is
T
A
B
E
A
G
H
E
G
H
F
D
F
E
C
D
T
C
B
C
T