Traveling Salesman and Chinese Postman problems 1. Problem Description and Complexity 2. Theoretical Approach 3. Practical Approaches and Possible Solutions 4. Examples

1. Graph Theory
Group 821
VGIS 8th Semester
Problem: Traveling Salesman / Chinese Postman

2. Agenda
➲
●
Introduction
Problem Description / Complexity
➲
Theoritical Aproach
➲
●
●
●
Possible Solutions-Algorithms / Practical Aproach
Greedy Shortest Path First
Pruning Cutting
Brute Force
➲
Example

3. Introduction
➲
Traveling Salesman Problem Description
●
●
➲
Problem Complexity
●
●
➲
➲
given a collection of cities and the cost of travel between
each pair, one has to find the cheapest way of visiting all
of the cities exactly once and returning to the starting
point.
TSP is one of the most intensely studied problems in
computational mathematics and yet no effective solution
method is known for the general case.
In the theory of computational complexity, the decision
version of the TSP (where, given a length L, the task is to
decide whether any tour is shorter than L) belongs to the
class of NP-complete problems.
given a starting city, we have n-1 choices
● for the second city, n-2 choices
● for the third city, etc.
(n-1)! = n-1 x n-2 x n-3 x. . . x 3 x 2 x 1
(n-1)! / 2 { cost != direction, symmetric TSP}

4. Theoretical Approach
➲
TSP can be modeled as an undirected weighted graph
➲
Cities are the graph's vertices
➲
Paths are the graph's edges
➲
Path's distance is edge's length
➲
TSP tour becomes a Hamiltonian cycle
➲
optimal TSP tour is the shortest Hamiltonian cycle

5. Greedy Shorthest Path First...

6. Pruning Cutting...

7. ...Brute Force

8. Examples
➲
1st Example
➲
2nd Example
?