They are from course Algorithms and Data Structures writted by Panos Louridas, Department of Management Science and Technology, Athens University of Economics and Business.

You can find the assignment here.

In this programm we must schedule the tournament so that each competitor has only one match each day. The program read a file from command prompt like: python plan_matches.py graph_file

• The graph_file in the form:

a b
a c
b c
c d
d e
e c
...

Example: For the file example_graph.txt python plan_matches.py graph_file_1.txt the output is:

(a, b) 0
(a, c) 1
(b, c) 2
(c, d) 0
(c, e) 3
(d, e) 1

More information:

• The problem that we described is called edge 'colouring problem'

• You can find more at wikipedia's [article] (https://en.wikipedia.org/wiki/Edge_coloring)

You can find the assignment here.

The program read a file from command prompt like python community_structure.py [-n GROUPS ] graph_file and detects community structure in networks.

• The graph_file in the form:

1 3
1 10
2 3
4 10
...

• The GROUPS is the number of the team we want to segmentate. If we don't write any number then it's mean 2 teams.

Example: For the file example_graph_1.txt python community_structure.py 3 example_graph_1.txt the output is:

[1, 2, 3, 10]
[4, 5, 6]
[7, 8, 9]
Q = 0.4896
( Q is the segmentation)

More information:

• The algorithm that we use at the exercise was added by M. E. J. Newman at the article "Fast algorithm for detecting community structure in networks", Phys. Rev. E 69, 066133, 2004. You can find it here.

You can find the assignment here.

The program read a file from command prompt like python sts.py n creates a list with all blocks sorted, and their number.

• A Steiner system with parameters t, k, n, written S(t,k,n), is an n-element set S together with a set of k-element subsets of S (called blocks) with the property that each t-element subset of S is contained in exactly one block.

Example: python sts.py 9 the output is:

[(1, 2, 8), (1, 3, 5), (1, 4, 6), (1, 7, 9), (2, 3, 6), (2, 4, 7), (2, 5, 9), (3, 4, 9), (3, 7, 8), 
(4, 5, 8), (5, 6, 7), (6, 8, 9)]
12

More information:

• More information about Steiner systems you can find at this article of Wikipedia.
• you can also see this link about steiner. (http://mathworld.wolfram.com/SteinerTripleSystem.html)

You can find it here.