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COMP36111 Advanced Algorithms 1 syllabus 2019-2020

COMP36111 materials

COMP36111 Advanced Algorithms 1

Level 3
Credits: 10
Enrolled students: 47

Course leader: Ian Pratt-Hartmann


Additional staff: view all staff

Requisites

  • Pre-Requisite (Compulsory): COMP11120
  • Pre-Requisite (Compulsory): MATH10101
  • Pre-Requisite (Compulsory): MATH10111
  • Pre-Requisite (Compulsory): COMP26120

Additional requirements

  • Students who are not from the School of Computer Science must have permission from both Computer Science and their home School to enrol.

    Pre-requisites

    To enrol students are required to have taken COMP26120 and one of the following:  COMP11120, MATH10101 or MATH10111.

Assessment methods

  • 70% Written exam
  • 30% Coursework
Timetable
SemesterEventLocationDayTimeGroup
Sem 1 Lecture 1.3 Tue 09:00 - 11:00 -
Themes to which this unit belongs
  • Programming and Algorithms

Overview

This course unit has two objectives. The first is to introduce the student to a range of fundamental, non-trivial algorthms, and to the techniques required to analyse their correctness and running-time.  The second is to present a conceptual framework for analysing the intrinsic complexity of computational problems, which abstracts away from details of particular algorithms.

Aims

This unit follows on from the material covered in COMP26111, focussing more particularly on mathematical analysis rather than on practical implementation. It is divided into two parts. The first considers a collection of important algorithms and analyses their complexity.

Topics considered include finding components in graphs, computing optimum flows in networks, matching in bi-partite graphs, solving the stable marriage problem, and string matching in text.

The second part considers the more general problem of analysing the intrinsic complexity of computational problems. Topics considered include the Turing model of computation and its associated complexity hierarchy, hardness and reductions, and both upper and lower complexity-bounds for various well-known problems from logic and graph theory.
There are two pieces of assessed coursework, and an exam at the end.

Syllabus

Part I (up to reading week): Algorithms
    Directed graphs: Tarjan's algorithm and topological orderings
    Undirected graphs: union find and the inverse Ackerman function
    Flow optimization and matching
    The stable marriage problem and the Gale-Shapley algorithm
    String matching and the KMP algorithm.
 
Part II (after reading week): Complexity
    Turing Machines and computational complexity     
    Some problems from logic: upper bounds
    Hardness and reductions: Cook's theorem
    Some problems from graph theory: 3-colouring, Hamiltonian and Eulerian circuits, the TSP
    Some problems from logic: lower bounds
    Savitch's theorem and the Immerman-Szelepcsényi theorem
    How to pass the exam.

Coursework

36111-cwk1-F-Formulating Arguments; Out of 20; Deadline End Wk II Oct 4th 14:00

36111-cwk2-S-exercisesA; Out of 20; Deadline End Wk IV Oct 18th 14:00

36111-cwk3-S-exercisesB; Out of 20; Deadline End Wk IX Nov 22nd 14:00

Deadlines

36111-cwk1-F-Formulating Arguments; Out of 20; Deadline End Wk II Oct 4th 14:00 36111-cwk2-S-exercisesA; Out of 20; Deadline End Wk IV Oct 18th 14:00 36111-cwk3-S-exercisesB; Out of 20; Deadline End Wk IX Nov 22nd 14:00

Teaching methods

Lectures

22 lecture course but some lectures will be cancelled to provide time for assessed exercises.

Feedback methods

Two pieces of assessed coursework during the course unit.

Study hours

  • Lectures (22 hours)

Employability skills

  • Analytical skills
  • Innovation/creativity
  • Problem solving

Learning outcomes

On successful completion of this unit, a student will be able to:

  • Reproduce a range of standard algorithms in Computer Science, and reason about their correctness and computational complexity.
  • Define the notions complexity class (such as PTIME and NPTIME), completeness and hardness, and compare complexity classes by reduction.
  • Show that some tasks are NP-complete and give a range of NP-complete problems.
  • Explain the hierarchy of complexity classes (including deterministic and non-deterministic classes, and time- and space-classes) and prove some of the key theorems concerning these classes.

Reading list

TitleAuthorISBNPublisherYearCore
Introduction to the theory of computation (3rd edition)Sipser, Michael9781133187813Cengage Learning2013
Algorithm design and applicationsGoodrich, Michael T. and Roberto Tamassia9781118335918Wiley2014

Additional notes

Course unit materials

Links to course unit teaching materials can be found on the School of Computer Science website for current students.