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Chinese postmanproblemBy: Ansis, Chirag and Eugene

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Background information

The Chinese postman problem, also known as the route inspectiona problem in the area of graph theory.

Suppose there is a mailman who needs to delier mail in a certain

neighbourhood. The mailman wants to limit the distance he must co

must make sure he can coer all the streets and at the same time a

at the starting point.

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Task

To find the minimum distance re!uired to

across all edges of an area while still ma

to finish at the starting point.

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E"ample:

#ind the min

distance tra

and the route

allows a post

reach all area

map and retu

the post offic

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Chosen limited area:

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$easuring %eight of &ode

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Changing isual representation of route

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'rocess (Step )*

To pick an area that thegroup wanted to study

and identify all the edges

and ertices. +ur chosendistrict in ong -ong

was Causeway Bay.

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'rocess (Step )*

 All the pathwayswere laid out.

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'rocess (Step *

 After identifying theertices and edges,

the pathways were

laid out in a

simplified manner.

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'rocess (Step /*

 A section of Causeway Bay was selected and used as an e"ample.consisted of ) ertices with odd number of nodes.

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'rocess (Step 0*

%e need to make the route Eulerian (such that the traeler returns

original point* by adding e"tra nodes. This makes all odd ertices e

There should be e"tra nodes that minimise the e"tra distance need

 A piece of software was used to determine this. (Thank you $r. Chi

&ote: A ma"imum of ) ertices with odd nodes was used because

ertices with odd nodes would take the computer too long to sole.

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'rocess (Step 0*

&odes connecting toodd ertices:

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'rocess (Step 0*

The e"tra nodes re!uired:

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'rocess (Step 2*

 A new route is created with the e"tra no

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3oute

 A) B) C) 4) 4 C C) 4) 4 4/ B/ B C C/ C0 B0 B/ B B) A) B

E) E E/ E E) E0 E) B2 A)

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'roblems Encountered

). $easuring the weights of each node was nprecise.

. The number of ertices with odd nodes app

be too numerous for computer to resole.

/. 6nterpreting the layout of the routes was diff

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Solution

). The measurements conducted had to be roup to account for inaccuracy.

. &umber of ertices with odd nodes was lim

ma"imum of ). &umber of possibilities of pis )7, /82.

/. The routes were redrawn in a more organis

manner.

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The end

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