MA428      Half Unit
Combinatorial Optimisation

This information is for the 2021/22 session.

Teacher responsible

Dr Katerina Papadaki


This course is available on the MSc in Applicable Mathematics and MSc in Operations Research & Analytics. This course is not available as an outside option.


Some familiarity with graph theory and some knowledge of linear programming is desirable. For students that have no linear programming background, it is recommended that they read the material of the first four lectures of course MA423, which can be found on the Moodle page of MA423.

Course content

The course is intended as an introduction to discrete and combinatorial techniques for solving optimisation problems, mainly involving graphs and networks. Topics covered include: minimum spanning trees; shortest path algorithms; maximum flow algorithms; minimum cost flow problems; matching and assignment problems; and other topics that may vary from year to year.


This course is delivered through a combination of seminars and lectures totalling a minimum of 30 hours across Lent Term. Depending on circumstances, seminars might be online.

Formative coursework

Students will be expected to produce 3 problem sets in the LT.

Students will be given weekly exercises. Oral feedback will be provided in the seminars, where the weekly homework will be discussed. Three of these weekly exercises will be handed in as formative coursework and the students will be given written feedback on their submissions.

Indicative reading

Lecture notes will be supplied for all topics.

Most of the lectures will be based on topics from:

R K Ahuja, T L Maganti and J B Orlin, Network Flows (2013).

William J. Cook, William H. Cunningham, William R. Pulleyblank, Alexander Schrijver, Combinatorial Optimization (1997).


Exam (100%, duration: 3 hours) in the summer exam period.

Course selection videos

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

Important information in response to COVID-19

Please note that during 2021/22 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the differing needs of students in attendance on campus and those who might be studying online. For example, this may involve changes to the mode of teaching delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Mathematics

Total students 2020/21: 35

Average class size 2020/21: 18

Controlled access 2020/21: Yes

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

  • Problem solving
  • Application of numeracy skills
  • Specialist skills