Lecturer	James Worrell
Degrees	Schedule S1(3rd years) — Computer Science Schedule B1 — Computer Science Schedule B1(M&CS) — Mathematics and Computer Science
Term	Hilary Term 2011  (16 lectures)

Overview

This 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 such as primality testing, linear optimisation and string matching. Students are also introduced to randomised algorithms and to techniques of amortised complexity analysis. As in the first-year course, the style of the presentation is rigorous but not formal.

Learning outcomes

On successful completion of the course students will:

• Be able to carry out amortised analysis of data structures, including splay trees and disjoint sets
• Understand the implementation, complexity analysis and applications of algorithms for string matching, primality testing, max flow, linear programming and the discrete Fourier transform

Synopsis

• Amortised analysis (1.5 lectures)
• Disjoint sets / Union-find (2  lectures)
• Splay trees (1.5 lectures)
• Fast Fourier transform (1 lecture)
• String matching: Rabin-Karp and Knuth-Morris-Pratt algorithms (2 lectures)
• Primality testing: Miller-Rabin algorithm (2 lectures) 
• Network flow: Edmonds-Karp algorithm (2 lectures)
• Linear programming (3 lectures)
• Mergeable heaps (1 lecture)

Syllabus

Amortised analysis 

Splay trees

Mergable heaps (time permitting)

Disjoint sets / Union-Find

Primality testing (Miller-Rabin algorithm)

String matching (Rabin-Karp and Knuth-Morris-Pratt  algorithms)

Max-flow (Edmonds-Karp algorithm)

Linear programming (Simplex method and duality)

Fast Fourier transform

Reading list

The main text used in the course is:

• Thomas Cormen, Charles Leiserson, Ronald Rivest and Clifford Stein, Introduction to Algorithms, MIT Press, 2001 (second edition).

The following text is a useful alternative.

• S. Dasgupta, C.H. Papadimitriou, and U.V. Vazirani.  Algorithms, Mcgraw-Hill, 2006. 

Taking our courses

This form is not to be used by students studying for a degree in the Department of Computer Science, or for Visiting Students who are registered for Computer Science courses

Other matriculated University of Oxford students who are interested in taking this, or other, courses in the Department of Computer Science, must complete this online form by 17.00 on Friday of 0th week of term in which the course is taught. Late requests, and requests sent by email, will not be considered. All requests must be approved by the relevant Computer Science departmental committee and can only be submitted using this form.