Diagram 2
Calculations of possible ways used
by the school bus (orders of notes)
As it can be seen on the diagram 2, there are 8 nodes in
total on the route. Each node can have different orders of
edges which mean each point can have different numbers
of possible ways to be used by school bus. By calculating
the orders of the nodes, I will find the numbers of even and
odd vertices.
When the diagram is examined it can be easily seen that
e1 has 3 ways to be used, and e 2 has 4 ways to be used.
Let x be the order of the each node, we can represent the
numbers of edges as;
Node (vertex) Order of node
e1 3
e2 4
e3 4
e4 4
e5 2
e6 4
e7 2
e8 3
Table 1: nodes and order of nodes
As it can be seen on the table 1, there are two odd vertices
which disables the Eulerian trail to be applied on my school
bus’ way. Thus, I will use semi-Eulerian trail to minimize my
school bus’ route.
To find the minimum route, I will follow the following 5
main steps which are the main part of Chinese postman
algorithm below.
Step 1: I will list all odd vertices on the diagram.
Step 2: I will list all possible pairings of odd vertices.
Step 3: I will find the edges which connects the nodes with
minimum length.
Step 4: I will find the pairings for odd vertices and calculate
the minimum length.
Step 5: I will calculate the total Chinese postman route
which is the sum of all edges added to the total length
found in step 4. (Suffolk County Council)
If I apply the steps on my route, the representation can be
done like below;
Step 1: The odd vertices are e1 and e8
Step 2: There is only one way of pairing these odd vertices
which can be represented as AH when I label the e1 as point
A and e8 as point H.
Step 3: The shortest way to combine node e1 to node e8 is
using the edges between e1-e2, e2-e6 and e6-e8.
Step 4: visual representation of the shortest way from e1 to
e8 is represented on the diagram below.
Sum of the lengths of the roads that my school bus will
follow can be presented with the notification below.
As a result of the calculations, Chinese postman algorithm
shows only 1 way which provides me least time loss. Due
to the algorithm, the route of the school bus should follow
the order below.
e1 (starting point)-e4-e3-e7-e8-e3-e1-e2-e4-e6-e2-e5-e6-
e8-e6-e2 and e1 (last point)
Total length of the shortest road is= 4245 meters.
To minimize the time loss during my school bus journey,
I tried to calculate the shortest route for my school bus
and according to my calculations and Chinese Postman
algorithm, the shortest route takes 4245 meters which
helps me to gain some more time.
The Green Wave System
Green Wave is a system which is used in arteries and
intersections to prevent drivers to be caught to red lights
one after another. That system provides a series of green
lights when drivers accord the speed limit of wave. By
this system traffic of big cities can be more fluent also this
system can decrease the level of Carbon dioxide emission
and provide fuel efficiency. Also that system promotes
people to accord speed limits and decrease over speeding.
In my exploration, I will find the most suitable speed limit for
the road that I use while I am going to school. Yavuz Sultan
Selim Boulevard is the road that I use every day to go to my
THE CLAPPER 2014 - 2015 36