# COMP36111 Advanced Algorithms 1 syllabus 2019-2020

COMP36111 materials

COMP36111 Advanced Algorithms 1

Level 3
Credits: 10
Enrolled students: 49

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

• 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

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.