Discrete mathematics - Graph theory and algorithms

linma1691  2019-2020  Louvain-la-Neuve

Discrete mathematics - Graph theory and algorithms
Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 22.5 h
Q1
Teacher(s)
Blondel Vincent; Delvenne Jean-Charles;
Language
French
Prerequisites
This courses assumes that the elementary notions of discrete mathematics are acquired such as taught in LEPL1108.
Main themes
Introduction to the language and theory of graphs : questions of characterization, isomorphism, existence and enumeration. Properties of directed and undirected graphs such as connectivity, planarity, k-colorability and the property of being Eulerian, perfect, etc. Modelling of practical problems : data structures and algorithms for the exploration of graphs. Basic graph algorithms and an analysis of their complexity.
Aims

At the end of this learning unit, the student is able to :

1 AA1 : 1,2,3
More precisely, by the end of the course the student will be able to :
  • model various problems in the language of graph theory
  • identify if a graph-theoretic problem has a known efficent algorithmic solution or not
  • propose and apply an algorithm to solve sucha a problem, at least for some classes of graphs
  • prove in a clear and rigorous fashion elementary properties related to the concepts covered in the course
 

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
Structure and characterization of graphs - basic concepts - degree, connected components, path, cycle, cut, minor, etc. Classes of graphs and their recognition - perfect, series parallel, planar graphs, acyclic digraphs, etc. Exploration of graphs and tests of their properties - k-connected, eulerian, etc. Flows - theorems of Menger and Hall, maximum flow and minimum cost flow algorithms and their complexity. Problems :finding optimal matchings and stable sets, the travelling salesman problem, cut, graph partitioning and graph colouring problems
Teaching methods
The course is organized in lessons and supervised exercise sessions.
Evaluation methods
The students are evaluated individually through a written exam based on the specific objectives described above.
Bibliography
Ouvrage de base :
Graph Theory with Applications, A. Bondy- U.S.R. Murty, Springer, téléchargement libre
Aussi :
  • Algorithmic Graph Theory, Alan Gibbons, Cambridge University Press 1985
  • Introduction to Graph Theory, Douglas West, Prentice Hall 1996.
  • Combinatorial Optimization, W.R. Cook et al., Wiley 1998.
  • Network Flows, Ahuja et al., Prentice Hall 1993.
Faculty or entity
MAP


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Aims
Additionnal module in Mathematics

Minor in Engineering Sciences: Applied Mathematics (only available for reenrolment)

Specialization track in Applied Mathematics

Minor in Applied Mathematics

Master [120] in Electrical Engineering

Master [120] in Computer Science

Master [120] in Statistic: General

Master [120] in Computer Science and Engineering