Combinatorial Optimisation

**This information is for the 2019/20 session.**

**Teacher responsible**

Neil Olver

**Availability**

This course is available on the MSc in Applicable Mathematics and MSc in Operations Research & Analytics. This course is available with permission as an outside option to students on other programmes where regulations permit.

**Pre-requisites**

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 two 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, with a brief introduction to matroids; shortest path algorithms; maximum flow algorithms; minimum cost flow problems; matching and assignment problems; and other topics that may vary from year to year.

**Teaching**

20 hours of lectures and 15 hours of seminars in the LT. 3 hours of lectures in the ST.

**Formative coursework**

Weekly exercises will be given that will be solved and discussed during the seminars. Two of those exercises will be handed in as formative coursework and the students will be given feedback on their submissions.

**Indicative reading**

Lecture notes will be supplied for most topics; otherwise reading from books will be indicated.

Most of the lectures will be based on topics from: R K Ahuja, T L Maganti and J B Orlin, Network Flows (2013).

**Assessment**

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

**
Key facts
**

Department: Mathematics

Total students 2018/19: 29

Average class size 2018/19: 29

Controlled access 2018/19: No

Value: Half Unit

**Personal development skills**

- Problem solving
- Application of numeracy skills
- Specialist skills