# DM817: Network Programming: Theory and Applications

Study Board of Science

Teaching language: Danish, but English if international students are enrolled

EKA: N340083102

Censorship: Second examiner: External

Grading: 7-point grading scale

Offered in: Odense

Offered in: Autumn

Level: Master's level course approved as PhD course

STADS ID (UVA): N340083101

ECTS value: 10

Date of Approval: 02-03-2020

Duration: 1 semester

Version: Approved - active

## Comment

15005701 (former UVA) is identical with this course description.

The course is offered as needed and is not necessarily offered every year. Examination for DM817 are offered according to the following plan when the course is offered: Ordinary examination (January), first re-examination (March) and 2nd re-examination in (June).

Examination for DM817 (part of courses offered E20) are offered: Ordinary examination January 2021, first re-examination March 2021 and 2nd re-examination in June 2021.

## Entry requirements

## Academic preconditions

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

## Course introduction

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.

## Expected learning outcome

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.

## Content

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

## Literature

## Examination regulations

## Exam element a)

## Timing

January

## Tests

## Project assignments

## EKA

N340083102

## Censorship

Second examiner: External

## Grading

7-point grading scale

## Identification

Student Identification Card

## Language

Normally, the same as teaching language

## Duration

Reexamination is an oral presentation - 60 minutes

## Examination aids

A closer description of the exam rules will be posted in itslearning.

## ECTS value

10

## Additional information

Reexam is an oral presentation.

## Indicative number of lessons

## Teaching Method

The teaching method is based on three phase model.

- Intro phase: 40 hours
- Skills training phase: 26 hours, hereof tutorials: 26 hours.

Activities during the study phase:

- 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.

## Additional teachers

Name | Department | City | |
---|---|---|---|

Jørgen Bang-Jensen | jbj@imada.sdu.dk | Institut for Matematik og Datalogi, Datalogi |