Chinese Postman Algorithm Aims: To be able to use the Chinese Postman Algorithm for: all even vertices. 2 odd vertices. Starting and ending at the same.

Chinese Postman Algorithm

Aims:To be able to use the Chinese Postman Algorithm for:

• all even vertices.• 2 odd vertices.

• Starting and ending at the same point.•Starting and ending at different points.

Non-Eulerian Semi-Eulerian Eulerian

Notes

• Eulerian Trails:– All vertices are even. –All edges used only

once.– Starting and ending at

the same place.

• Semi-Eulerian Trails:– 2 odd vertices.– All edges used only

once.– Start and end at the

odd vertices.

• Non-Eulerian Trails:–More than 2 odd vertices.

– Some edges will need to be used twice.

All Even Vertices Example

2 Odd Vertices Example

Question 1

Question 2

Question 3

Question 4

4 Odd Vertices

• This is the most common type of exam question.

• You need to consider the weight all possible pairs of odd vertices.

• Choose the two pairs with the shortest total weight.

• You can then use this result to solve the problem.

4 Odd Vertices Example

Possible Pairs Shortest Paths Weights

and and + =

and and + =

and and + =