Un continuum du lycée à l’université
Présentation des projets de recherche
2012>2020
Date
2
LIFO et Lycée Voltaire
Doctorant : Pedro MONTEALEGRE
Lycéens : Nathan CAM, Dimitri CORDAT,
Vincent DESCHAMPS, Hiba EL YACHKOURI,
Pierre-Alexandre PERON
3
Lycée Voltaire
4
Lab : LIFO
5
Pedro Montealegre
PhD in computer science (Informatique)
Title: Complexity of distributed algorithms
in graphs.
6
7
Graph
8
Graph
1
2
Vertices
3
5
4
9
Graph
1
2
Vertices
Edges
3
5
4
10
Size
1
2
3
5
4
11
Size
1
2
Neighbors
3
5
4
12
2
Size
2
1
2
Neighbors
Degree
3
3
2
1
5
4
13
1
Complete Graph
1
4
2
3
1
2
4
3
2
3
5
14
1
Complete Graph
1
4
2
3
1
2
2
3
5
2
4
3
15
Problem: Graph Coloring
Each vertex have a color
Adjacent vertices must have different
colors
Task: color the graph with the minimum
number of colors
16
Graph Coloring
1
2
3
4
5
17
Graph Coloring
1
2
3
4
5
18
Graph Coloring
1
2
3
4
5
19
Graph Coloring
1
2
3
4
5
20
Dimitri
Hiba
Nathan
Math Club
X
X
X
Debate Club
X
Pierre A.
Pedro
X
X
Science
Club
X
X
Comp. Club
X
Art Club
French Club
Vincent
X
X
X
21
FC
SC
MC
CC
DC
AC
22
FC
SC
MC
CC
DC
AC
23
Coloring problem :
We have a big graph, and we want to know
if it can be colored with 5 colors.
24
25
Graph algorithms for coloring
« Brute Force » : Test every possible
coloration
26
Graph algorithms for coloring
« Brute Force » : Test every possible
coloration
If the graph is of size 150 and we want to know if
it can be colored with 5 colors, we need to test
5150 possible colorations
5150 > 7 x 10104
(number atoms in the universe < 1080)
27
Graph algorithms for coloring :
Welsh and Powell (aproximated) Algorithm
1
4
6
3
2
5
28
Welsh and Powell Algorithm
1
4
6
3
2
5
29
Welsh and Powell Algorithm
(1) Sort the vertices from the highest degree to the lowest.
1
4
6
3
2
5
30
Welsh and Powell Algorithm
(1) Sort the vertices from the highest degree to the lowest.
4, 1, 2, 6, 3, 5
1
4
6
3
2
5
31
Welsh and Powell Algorithm
(2) Paint the highest uncolored vertex with a new color
4, 1, 2, 6, 3, 5
1
4
6
3
2
5
32
Welsh and Powell Algorithm
(3) Go down the list painting with the current color
4, 1, 2, 6, 3, 5
1
4
6
3
2
5
33
Welsh and Powell Algorithm
(3) Go down the list painting with the current color
4, 1, 2, 6, 3, 5
1
4
6
3
2
5
34
Welsh and Powell Algorithm
(4) If every vertex is colored we are done, if not, go back to step (2)
4, 1, 2, 6, 3, 5
1
4
6
3
2
5
35
Welsh and Powell Algorithm
4, 1, 2, 6, 3, 5
1
4
6
3
2
5
36
Welsh and Powell Algorithm
4, 1, 2, 6, 3, 5
1
4
6
3
2
5
37
Welsh and Powell Algorithm
4, 1, 2, 6, 3, 5
1
4
6
3
2
5
38
Welsh and Powell Algorithm
4, 1, 2, 6, 3, 5
1
4
6
3
2
5
Conclusion
Merci pour
votre attention