# ADVANCED ALGORITHMS - 2023/4

Module code: COM2031

## Module Overview

The module introduces algorithmic techniques for various sets of problems and teaches how to analyse algorithms in terms of their complexity. The techniques build upon the data structures and algorithms module provided in level 4 (COM1029) so that students can further develop their use of methods for solving complex problems.  Examples will be used throughout to demonstrate the relevance of each approach.

### Module provider

Computer Science

BAUER Roman (Elec Elec En)

## Overall student workload

Independent Learning Hours: 106

Lecture Hours: 22

Laboratory Hours: 22

Semester 1

None

## Module content

• Divide-and-Conquer

• Concepts of Divide-and-Conquer

• Selected problems and their solutions using Divide-and-Conquer

• Dynamic Programming

• Concepts of dynamic programming

• Selected problems and their solutions using dynamic programming

• Linear Programming

• Concepts of linear programming

• Simplex algorithm

• Selected problems and their solutions using linear programming

• Network Flow Problems

• Paths in graphs

• Max-flow/min-cut problem

• Min-cost flow problem (transportation problem)

• Algorithms for NP problems

• Reducibility and NP-completeness

• Selected NP problems and strategies for finding their solutions

• A selection of the following advanced topics:

• Number-Theoretic Algorithms, Modular arithmetic (extended GCD, mod exponentiation, mod inversion, Cyclic Groups

• Cryptographic Algorithms, Integer factorization, Discrete Logarithms, Encryption algorithms.

• Approximation Algorithms

• Randomised Algorithms

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework INDIVIDUAL COURSEWORK 20
Examination Online ONLINE (OPEN BOOK) EXAM WITHIN 4HR WINDOW 80

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate that they have achieved the module learning outcomes.

Thus, the summative assessment for this module consists of:

·         An individual coursework on sets of problems that students are required to solve. This addresses LO1, LO2, LO3, LO4 and LO5.

·         A 4h unseen open-book online examination on the whole course content. This addresses LO2, LO3, L05 and LO6.

The individual courseworks will be due around week 6. The exam takes place at the end of the semester during the exam period.

Formative assessment and feedback

Lecture slides are used extensively in the lectures with each lecture consisting of a number of slides explaining the theory and showing the examples. Solutions to lab exercises are explained during the lab session and provided to the students as part of preparation for the exam.

## Module aims

• The aim of this module is to equip students with a tool box of efficient algorithmic techniques which they can apply to real-world problems. This will cover foundations, theoretical advantages and constraints of a broad range of algorithms. Mathematical algorithms and operational techniques will be presented using examples of problems allowing students to practice their application. Appropriate mathematical concepts will be introduced to support the theoretical design and evaluation of algorithms.

## Learning outcomes

 Attributes Developed 1 Understand the distinctive features of a broad range of algorithmic techniques that can be used to solve real-world problems KC 2 Formulate problems as abstract models which can be solved by generic algorithms and mathematical methods KC 3 Critically evaluate the design and efficiency of algorithms for specific types of problem KCT 4 Execute and implement algorithms in a programming language. 5 Apply a range of appropriate algorithms to example problems KPT 6 Critically interpret the performance of an algorithm and identify improvements that can be applied to make them more efficient KPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• Help students understand the distinctive features of a broad range of algorithmic techniques

• Deomonstrate the application of algorithmic techniques for solving concrete problems

• Explain students how to analyse the complexity of an algorithm, incl. its performance and how to compare different algorithms

• Equip students with necessary mathematical background to understanding certain algorithms

• Enable students to apply taught techniques to solve concrete problems

The learning and teaching methods include:

• Lectures (11 weeks at 2h) using detailed lecture slides to gauge the students’ understanding

• Labs/Tutorials (11 weeks at 2h) using exercises and their solutions and demonstrations.

Students will be expected to spend a minimum of 7 hours a week on self-study to prepare and revise lecture, lab and tutorial material.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.