Introductory description

This module is concerned with studying properties of graphs and digraphs from an algorithmic perspective.
This module is only available to students in the second year of their degree and is not available as an unusual option to students in other years of study.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Typical topics include:
Introduction to graphs: undirected graphs, directed graphs, weighted graphs, graph representation and special classes of graphs (trees, planar graphs etc.).
Applications of graphs (in telecommunications, networking etc.).
Basic algorithmic techniques for graph problems: graph traversals (DFS and BFS), topological sorting, Eular tours.
Further algorithmic problems on graphs: minimum spanning trees, shortest path problems, matching problems.
Planar graphs and their properties. Eular's formula, planar separateor theorem and their algorithmic applications.
Further optimization problems on graphs including graph colouring and graph questions in distributed systems.
Discussing practical applications of graphs and efficient algorithms for such practical problems. Approximation algorithms and heuristic algorithms. Applications to searching in massive graphs (e.g. page ranking); use of structural properties and algebraic properties.

Learning outcomes

By the end of the module, students should be able to:

• - Understand the basics of graphs, directed graphs, weighted graphs, and be able to relate them to practical examples.
• - Use effectively algorithmic techniques to study basic parameters and properties of graphs.
• - Design efficient algorithms for various optimisation problems on graphs.
• - Use effectively techniques from graph theory to approach practical problems in networking and telecommunication.

Indicative reading list

Please see Talis Aspire link for most up to date list.

View reading list on Talis Aspire

Subject specific skills

Acquiring basic knowledge in the new area (of algorithmic graph theory), including learning the key concepts of mathematical rigour in the analysis of graph algorithms, of the proofs of correctness of algorithms, and of the efficiency of algorithms.
An important part of the module will be to focus on mathematical properties of graphs and networks, as a tool to the design of better algorithms.

Transferable skills

Critical thinking and creativity.
Communication: presentation skills, focusing on mathematical-style presentation (students will have to prepare a short presentation describing some of the topics from the module).