Advanced Algorithms
Principal lecturer: Dr Thomas Sauerwald
Taken by: Part II CST 50%, Part II CST 75%
Hours: 12
Suggested hours of supervisions: 3
Prerequisites: Algorithms
Past exam questions
Aims
The aim of this course is to introduce advanced techniques for the design and analysis of algorithms that arise in a variety of applications. A particular focus will be on parallel algorithms, linear programming and approximation algorithms.
Lectures
- Sorting Networks. Zero-one principle. Merging Network, Bitonic Sorter. Counting Networks. [CLRS2, Chapter 27]
- Linear Programming. Definitions and Applications. Formulating Linear Programs. The Simplex Algorithm. Finding Initial Solutions. [CLRS3, Chapter 29]
- Approximation Algorithms. (Fully) Polynomial-Time Approximation Schemes. Design Techniques. Applications: Vertex Cover, Subset-Sum, Parallel Machine Scheduling, Travelling Salesman Problem (including a practical demonstration how to solve a TSP instance exactly using linear programming), Hardness of Approximation. [CLRS3, Chapter 35]
- Randomised Approximation Algorithms. Randomised Approximation Schemes. Linearity of Expectations and Randomised Rounding of Linear Programs. Applications: MAX3-SAT problem, Weighted Vertex Cover, Weighted Set Cover. Summary: MAX-SAT problem and discussion of various approximation algorithms. [CLRS3, Chapter 35].
Objectives
At the end of the course students should
- have an understanding of algorithm design for parallel computers;
- be able to formulate, analyse and solve linear programs;
- have learned a variety of tools to design efficient (approximation) algorithms.
Recommended reading
* Cormen, T.H., Leiserson, C.D., Rivest, R.L. and Stein, C. (2009). Introduction to Algorithms. MIT Press (3rd ed.). ISBN 978-0-262-53305-8