The document discusses the Chinese Postman Problem, which involves finding the shortest route for a postman to deliver mail to every address on a graph. It introduces the problem, models it using a directed graph with edges representing streets and nodes representing intersections, and outlines the algorithm for solving it. The algorithm involves classifying the graph as Eulerian, trial, or semi-Eulerian and using different approaches depending on the classification to find an optimal solution.

1. Computational
Thinking
10: Chinese Postman Problem

2. Outline
1. Introduction
2. Application of the Model
3. Model Formulation
4. Algorithm for Solution
5. Illustration of Running Algorithm

3. 1. Introduction
- The Chinese Postman Problem was first
posed by a Chinese mathematician in
1962. It involved trying to calculate how a
postman could best choose his route so as
to minimize his time.
• This is the problem that he tried to solve:
• How could a postman visit every letter on
the graph in the shortest possible time?

5. Route Inspection Problem

6. The Route of the Postman
- Postman Tour or Route Inspection Problem, is a famous problem in Graph
Theory: The postman's job is to deliver all of the town's mail using the
shortest route possible. In order to do so, he (or she) must pass each street
once and then return to the origin.
-We model this problem using a directed
graph. Edges and nodes represent streets
and intersections, respectively. The length
of a street is represented by the weight of
the corresponding edge. By using directed
edges, it's possible to also account for one-
way-streets etc in the graph

7. 2. Application of the Model

10. 3. Model Formulation

11. Drilling down the problem

12. 4. Algorithm of the Problem

13. Connected non-oriented Network

14. Classification of the Problem
Eulerian
Trial
Semi
Eulerian
4 Odd Vertices

15. Existing of
Solution

16. Chinese Postman
Algorithm

17. Example-1

18. Example-2

19. 5. Illustration of Running Algorithm

20. Checking for Existing of Feasible Solution

21. Optimal Solution

22. References
1. https://www.slideshare.net/ocusadu/chinese-postman-problem-non-oriented-network
2. https://www-m9.ma.tum.de/graph-algorithms/directed-chinese-postman/index_en.html
3. https://studylib.net/doc/5438441/chinese-postman-problems
4. https://www.slideserve.com/jon/route-inspection