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Chinese Postman algorithm

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by

Molly Bennett

on 10 July 2014

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Transcript of Chinese Postman algorithm

Chinese post man
Firstly before starting my project i needed to research what exactly the chinese post man algorithm was. My main source of information was obtained from (www.suffolkmaths.co.uk/pages/Maths%20Projects/Projects/Topology%20and%20Graph%20Theory/Chinese%20Postman%20Problem.pdf) which i felt gave me the knowledge that i needed to complete my project in a clear and easily understandable way.

Initially I chose to investigate the best route to take when traveling to all of the counties in England.
I began creating my network and finding out the distances between the adjoining counties
After doing this I counted how many
vertices each point had,
in order to decipher the odd from
the even.
Traveling North
Therefore I chose to investigate the best route to take when wanting to travel to all of the counties in the north or north midlands of England. This allowed me to create a much more simplified map that was easier for me to find the perfect route.
Chinese Postman algorithm
Traveling North
by Molly Bennett

I then identified that there were 16 counties that were odd. However when it came to putting them into possible pairings, by using the formula i found out that the possible pairings to work out would possibly be too high of a number for me to work out. This lead me to reformulate by initial idea for my project.
The fastest way from C (Durham) to H (Nottinghamshire) is using the path CD, DH- which gives a total length of 96.7.
This means that the optimal chinese postman route is the sum of all the edges plus 96.7, which equals
1158.8.
By drawing the extra edges this made the graph Eulerien and thus I was able to plan a route that would start and end in the same position (at A).

This means that the optimum route is
ABCDIHDGHDEFGDEADCA
The solution I obtained will allow for travel in the shortest time around all 9 counties. However there are alot of paths that have to be repeated such as D (which is repeated 4 times) which may not be the most convenient. Moreover my solution does not take into account external factors that may contribute to a change in distance or time between two counties. This includes road changes, traffic jams and other issues that may make the journey longer. Moreover by using google maps to get distances between counties, the measurements achieved are unlikely to be completely accurate, and this intern could have effected my result.
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