Advanced Algorithms 1
|Unit level:||Level 3|
|Teaching period(s):||Semester 1|
|Offered by||School of Computer Science|
|Available as a free choice unit?:||Y
Additional RequirementsStudents who are not from the School of Computer Science must have permission from both Computer Science and their home School to enrol.
To enrol students are required to have taken COMP26120 and one of the following: COMP11120, MATH10101 or MATH10111.
This unit provides an advanced course in algorithms, assuming the student already knows algorithms for common computational tasks, and can reason about the correctness of algorithms and understand the basics of computing the complexity of algorithms and comparing algorithmic performance.
The course focuses on the range of algorithms available for computational tasks, considering the fundamental division of tractable tasks, with linear or polynomial-time algorithms, and tasks that appear to be intractable, in that the only algorithms available are exponential-time in the worst case.
To examine the range of algorithmic behaviour and this fundamental divide, three topics are covered:
- Examining a range of common computational tasks and algorithms available: We shall consider linear and polynomial-time algorithms for string matching tasks and problems that may be interpreted in terms of graphs. For the latter we shall consider the divide between tractable and intractable tasks, showing that it is difficult to determine what range of algorithms is available for any given task.
- Complexity measures and complexity classes: How to compute complexity measures of algorithms, and comparing tasks according to their complexity. Complexity classes of computational tasks, reduction techniques. Deterministic and non-deterministic computation. Polynomial-time classes and non-deterministic polynomial-time classes. Completeness and hardness. The fundamental classes P and NP-complete. NP-complete tasks.
Advanced Algorithms (II): In the second semester a follow-up course unit is available. This course will explore classes of algorithms for modelling and analysing complex systems, as arising in nature and engineering. These examples include: flocking algorithms; optimisation algorithms; stability and accuracy in numerical algorithms.
OverviewThis course unit has two objectives. The first is to introduce the student to a range of advanced algorithms for difficult computational problems, including matching, flow networks and linear programming. The second objective is to ouline the mathematical techniques required to analyse the complexity of computational tasks in general. There are two pieces of assessed coursework, and an exam at the end.
Teaching and learning methods
22 lecture course but some lectures will be cancelled to provide time for assessed exercises.
Learning outcomes are detailed on the COMP36111 course unit syllabus page on the School of Computer Science's website for current students.
- Analytical skills
- Problem solving
- Written exam - 75%
- Written assignment (inc essay) - 25%
Part I (up to reading week): Algorithms
- The stable marriage problem
- Basic graph algorithms
- Flow optimization and matching
- Boyer-Moore and Knuth-Morris-Pratt algorithms
- Linear programming
- Integer programming
- Review of Coursework I
Part II (after reading week): Complexity
- Turing Machines and computability (review)
- Problems and complexity classes
- Propositional satisfiability
- Hardness and reductions
- Graph-theoretic problems
- Quantified Boolean Formulas
- Savitch's Theorem
- The Immerman-Szelepcsenyi theorem
- Review of Coursework II
There will be two coursework exercises details of which can be found on the course unit materials page.
COMP36111 reading list can be found on the School of Computer Science website for current students.
Feedback methodsTwo pieces of assessed coursework during the course unit.
- Lectures - 22 hours
- Independent study hours - 78 hours