Master's level course approved as PhD course

The course is offered when needed.

To be announced.

Jørgen Bang-Jensen, Professor, lic.scient., dr. scient

Tlf.: 6550 2335 Email: jbj@imada.sdu.dk

Group | Type | Day | Time | Classroom | Weeks | Comment |
---|---|---|---|---|---|---|

Common | I | Monday | 14-16 | IMADA semi | 15 | |

Common | I | Monday | 12-16 | IMADA semi | 17 | |

Common | I | Monday | 12-14 | IMADA semi | 18 | |

Common | I | Tuesday | 14-16 | IMADA semi | 12 | |

Common | I | Wednesday | 12-14 | IMADA semi | 12 | |

Common | I | Wednesday | 14-16 | IMADA semi | 15-16 | |

Common | I | Thursday | 10-12 | U7 | 5,8-11 | |

Common | I | Thursday | 10-12 | IMADA semi | 6-7,16 | |

Common | I | Friday | 11-13 | IMADA semi | 5-11 | |

H1 | TE | Monday | 09-11 | U155 | 6 | |

H1 | TE | Monday | 10-12 | IMADA semi | 7-8 | |

H1 | TE | Monday | 14-16 | IMADA semi | 16 | |

H1 | TE | Wednesday | 12-14 | IMADA semi | 9-11 | |

H1 | TE | Thursday | 12-14 | IMADA semi | 5,15 | |

H1 | TE | Thursday | 10-12 | U153 | 12 | |

H1 | TE | Thursday | 10-12 | IMADA semi | 18 | |

H1 | TE | Friday | 10-12 | IMADA semi | 16 |

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Ubegrænset deltagerantal

None

Students taking the course are expected to:

- Have knowledge basic algorithms such as those taught in DM507.
- Have knowledge of basic mathematical argumentation including mathematical induction and proof by contradiction.
- Have knowledge about complexity of algorithms.
- Have knowledge of basic datastructures such as those taught in DM507

The aim of the course is to enable the student to:

- Apply flow methods as an important tool for solving practical optimization problems. Besides standard flow problems, examples are matching problems, orientation problems and simple scheduling problems.
- Model various optimization problems as flow problems.
- Apply the theory of flows to show that a given problem can be efficiently solved.
- Use flow theory to derive structural descriptions of optimal solutions for certain optimization problems.
- Explain the algorithms from the course and apply these to problems resembling those from the course.
- Formulate a (generalized) flow model from a problem description in words.
- Explain algorithms from the course in which flow algorithms form a subcomponent, e.g. increasing the edge-connectivity of digraphs, matchings in bipartite graphs and scheduling algorithms.

The course builds on the knowledge acquired in the courses DM507 Algorithms and data structures and DM553 Complexity and Computability.

The course gives a foundation for elective courses within combinatorial optimization and grafteoretical topics. The course also gives a solid foundation for writing a master thesis with the area of graph algorithms and all flow related areas.

In relation to the competence profile of the degree it is the explicit focus of the course to enable the student to:

- Analyze and solve advanced problems by use of flow methods.
- Develop new variants of the learned flow methods in order to apply these to new problems.
- Solve practical optimization problems by use of flow methods.

The learning objectives of the course is that the student demonstrates the ability to:

- Apply the theory of network flows as a tool for solving problems which resemble those from the course
- Apply flow algorithms as subroutines in more complex algorithms
- Evaluate whether one can model a given problem, resembling those from the course, as a flow problem.
- Argue about the complexity of algorithms which are based on flow algorithms.
- Explain generalizations of flows and explain by examples how these expand the range of applications of the theory.
- Apply the theory and algorithms from the course to solve practical optimization problems such as flow problems, transportation problems, matching problems, simple scheduling problems and orientation problems for (road) networks.

The following main topics are contained in the course:

- Shortest paths
- Flows and minimum cost flows
- Polynomial algorithms for flow problems
- Scheduling including project planning
- Flows with convex cost functions
- Submodular flows
- Graph connectivity
- Matchings in graphs
- Primal dual algorithms

- Meddeles ved kursets start

This course uses e-learn (blackboard).

None

- Project assignments. (10 ECTS). External marking, 7-mark scale.

Reexam is an oral presentation.

The teaching method is based on three phase model.

Intro phase: 40 hours

Skills training phase: 26 hours, hereof:

- Tutorials: 26 hours

- Solution of weekly assignments in order to discuss these in the exercise sections.
- Solving the project assigments
- Self study of various parts of the course material.
- Reflection upon the intro and training sections.

The intro phase consists of lectures by the teacher. Here we cover theory and methods and these are illustrated through examples. The intro phase is complemented by the skills training phase in which the students each week are working with new assigments covering the topics currently studied. Finally, the study phase consists of further independent reading of and reflection upon the course materials as well as solution of the two sets of problems which constitute the exam.

This course is taught in English, if international students participate. Otherwise the course is taught in Danish.

See deadline of enrolment.

See fees for single courses.