OverviewThis course builds on the first-year Design and Analysis of Algorithms course. It introduces students to a number of highly efficient algorithms and data structures for fundamental computational problems across a variety of areas. Students are also introduced to techniques such as amortised complexity analysis. As in the first-year course, the style of the presentation is rigorous but not formal. The lectures for this course are recorded, and the recordings will be released at the end of term.
On successful completion of the course students will:
- Understand the implementation, complexity analysis and applications of fundamental algorithms such as max flow and linear programming
- Be able to analyse and use some fundamental data structures, such as binary search trees and disjoint sets
- Have some familiarity with randomised algorithms, approximation algorithms, and fixed parameter algorithms
- Amortised analysis
- Disjoint sets / union-find
- Binary search trees (Red-Black trees, splay trees)
- Max flow and min cut in networks; applications
- Linear programming
- Approximation algorithms
- Fixed-parameter tractability
- Exponential algorithms
The main text used in the course is:
- Thomas Cormen, Charles Leiserson, Ronald Rivest and Clifford Stein, Introduction to Algorithms, MIT Press, 2009 (third edition).
Other useful textbooks that cover some of the material are
- S. Dasgupta, C.H. Papadimitriou, and U. V. Vazirani, Algorithms, Mcgraw-Hill, 2006.
- J. Kleinberg and E. Tardos, Algorithm Design, Addison-Wesley, 2006.
- V. Vazirani, Approximation Algorithms, Springer, 2001