1. The document describes the process of solving the travelling salesman problem using Giraph. It shows the graph and steps taken during supersteps 0-3. 2. In superstep 0, the source node sends out all possible paths and their costs to other nodes. In superstep 1-2, each node computes the lowest cost path from the source. 3. By superstep 3, the source has received all responses and identifies the overall minimum cost path by comparing values received.

1. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 24 24
30
10
12 12 32 32
1
33 33 31 31
On the left, we will show the original graph, to know how to process each step

2. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 24 24
30
10
12 12 32 32
1
33 33 31 31
Superstep 0 begins

3. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 24 24
30
10
12 12 32 32
1
33 33 31 31
Superstep 0 : we compute vertex n°1, nothing to do, it is not the source

4. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 24 24
30
10
12 12 32 32
1
33 33 31 31
Superstep 0 : we compute vertex n°2, the source

5. Giraph : Travelling Salesman Problem
Superstep : 0 1 2 3
23 23 24 24
30 2,12+30
10
12 12 32 32
1
2,12+1
33 33 31 31
The source sends all the possible paths and their values to the others nodes

6. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 24 24
30 2,12+30
10
12 12 32 32
1
2,12+1
33 33 31 31
The source then votes to halt

7. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 24 24
30 2,12+30
10
12 12 32 32
1
2,12+1
33 33 31 31
Superstep 0 : we compute vertex n°3, nothing happens as it is not the source

8. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 24 24
30 2,12+30
10
12 12 12 32 32
1
2,12+1
33 33 33 31 31
Superstep 1 begins

9. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 24 24
30 2,12+30
10
12 12 12 32 32
1
2,12+1
33 33 33 31 31
Superstep 1 : we compute vertex n°1

10. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 24 24
30 2,12+30
10
12 12 12 32 32
1
2,12+1 21,42+10+23
33 33 33 31 31
Superstep 1 : we compute vertex n°1

11. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 24 24
30 2,12+30
10
12 12 12 32 32
1
2,12+1 21,42+10+23
33 33 33 31 31
Superstep 1 : we compute vertex n°3

12. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 24 24
30 2,12+30 23,13+10+33
10
12 12 12 32 32
1
2,12+1 21,42+10+23
33 33 33 31 31
Superstep 1 : we compute vertex n°3

13. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 24
30 2,12+30 23,13+10+33
10
12 12 12 12 32
1
2,12+1 21,42+10+23
33 33 33 33 31
Superstep 2 begins

14. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 24
30 2,12+30 23,13+10+33
10
12 12 12 12 32
1
2,12+1 21,42+10+23
33 33 33 33 31
Superstep 2 : we compute vertex n°1

15. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 24
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 32
1
2,12+1 21,42+10+23
33 33 33 33 31
Superstep 2 : we compute vertex n°1

16. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 24
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 32
1
2,12+1 21,42+10+23
33 33 33 33 31
Superstep 2 : we compute vertex n°3

17. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 24
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 32
1
2,12+1 21,42+10+23
213,75+10+33=118
33 33 33 33 31
Superstep 2 : we compute vertex n°3

18. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 23
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 12
1
2,12+1 21,42+10+23
213,75+10+33=118
33 33 33 33 33
Superstep 3 begins

19. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 23
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 12
1
2,12+1 21,42+10+23
213,75+10+33=118
33 33 33 33 33
Superstep 3 : we compute vertex n°1

20. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 23
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 12
1
2,12+1 21,42+10+23
213,75+10+33=118
33 33 33 33 33
Superstep 3 : we compute vertex n°1 : votes to Halt

21. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 23
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 12
1
2,12+1 21,42+10+23
213,75+10+33=118
33 33 33 33 33
Superstep 3 : we compute the source, reactivated by the messages received

22. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 23
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 12
1
2,12+1 21,42+10+23
213,75+10+33=118
33 33 33 33 33
The source compares the values received and finds the minimum distance

23. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 23
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 109
1
2,12+1 21,42+10+23
213,75+10+33=118
33 33 33 33 33
and sets its value as the minimum

24. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 23
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 109
1
2,12+1 21,42+10+23
213,75+10+33=118
33 33 33 33 33
The source then votes to Halt

25. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 23
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 109
1
2,12+1 21,42+10+23
213,75+10+33=118
33 33 33 33 33
Superstep 3 : we compute vertex n°3

26. Giraph : Travelling Salesman Problem
0 1 2 3
23 23 23 23 23
30 2,12+30 23,13+10+33 231,56+30+23=109
10
12 12 12 12 109
1
2,12+1 21,42+10+23
213,75+10+33=118
33 33 33 33 33
Superstep 3 : we compute vertex n°3 : votes to Halt, ends the process