Dr Katerina Papadaki NAB 3.14

This course is available on the MSc in Applicable Mathematics and MSc in Management Science (Operational Research). This course is available as an outside option to students on other programmes where regulations permit.

Some familiarity with graph theory and some knowledge of programming could be desirable.

The course is intended as an introduction to discrete and combinatorial techniques for solving optimisation problems, mainly involving graphs and networks, as described under the headings of the lecture course below. MG4C6.1 “Foundations of Mathematical Programming”. is an introduction to the mathematical foundations of mathematical programming. MG408 “Combinatorial Optimisation” covers the topics: minimum spanning trees with a brief introduction to matroids, shortest path algorithms, maximum flow algorithms, minimum cost flow problems and matching problems and a choice of two other topics such as NP-completeness or approximation algorithms.

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

MG4C6.1 -  four LT; MG4C6.1A two x 1.5 LT.

MG408 - sixteen LT; MG408A eight x 1.5 LT and one revision session.

A reading week will take place in W6. There will be no teaching during this week.

Lecture notes will be supplied for most topics otherwise reading from books will be indicated. Weekly exercises will be given that will be solved and discussed during the seminars.

Most of the lectures will be based on topics from:Network Flows, Ahuja, Magnanti and Orlin

Also topics on NP-compleness and approximation algorithms if covered will be covered from the book: The Design of Approximation Algorithms, by David P. Williamson and David B. Shmoys

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