1. 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.

10. Non-EulerianSemi-EulerianEulerian

11. 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.

12. All Even Vertices Example

13. 2 Odd Vertices Example

14. Question 1

15. Question 2

16. Question 3

17. Question 4

18. 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.

19. 4 Odd Vertices Example Possible PairsShortest PathsWeights and += += +=