CS356-15 Approximation and Randomised Algorithms
Introductory description
The module aims to introduce students to the area of approximation and randomised algorithms, which often provide a simple and viable alternative to standard algorithms.
Module aims
Students will learn the mathematical foundations underpinning the design and analysis of such algorithms.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
- Linearity of expectation, moments and deviations, coupon collector's problem
- Chernoff bounds and its applications
- Balls into bins, hashing, Bloom filters
- The probabilistic method, derandomization using conditional expectations
- Markov chains and random walks
- LP duality, relaxations, integrality gaps, dual fitting analysis of the greedy algorithm for set
cover.
-The primal dual method: Set cover, steiner forest - Deterministic rounding of LPs: Set cover, the generalized assignment problem
- Randomized rounding of LPs: Set cover, facility location
- Multiplicative weight update method: Approximately solving packing/covering LPs
If time permits, more topics can be covered such as Tail inequalities for martingales, SDP based algorithms, local search algorithms, PTAS for Euclidean TSP, metric embeddings, hardness of approximation, online algorithms or streaming.
Learning outcomes
By the end of the module, students should be able to:
- 1. Understand and use suitable mathematical tools to design approximation algorithms and analyse their performance.
- 2. Understand and use suitable mathematical tools to design randomised algorithms and analyse their performance.
- 3. Learn how to design faster algorithms with weaker (but provable) performance guarantees for problems where the best known exact deterministic algorithms have large running times.
Indicative reading list
Please see Talis Aspire link for most up to date list.
View reading list on Talis Aspire
Subject specific skills
- Use of LP relaxations and related algorithm design paradigms in approximation algorithms
- Use of Chernoff bounds and related tools from discrete probability in randomised algorithms
- Systematic techniques for derandomising randomised algorithms
Transferable skills
- Communication - Reading and writing mathematical proofs
- Critical Thinking - Problem solving
- Technical - Technological competence and staying current with knowledge
Study time
| Type | Required |
|---|---|
| Lectures | 30 sessions of 1 hour (20%) |
| Seminars | 9 sessions of 1 hour (6%) |
| Private study | 111 hours (74%) |
| Total | 150 hours |
Private study description
Revision of lectures
Reading up on lecture notes and book chapters posted on the module webpage
Going through the problems solved during seminar sessions
Solving past exam papers
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group D2
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Homework Assignment | 20% | Yes (extension) | |
| In-person Examination | 80% | No | |
|
CS356 exam.
|
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Assessment group R1
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination - Resit | 100% | No | |
|
CS356 resit examination
|
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Feedback on assessment
- Marked scripts available on students' request
- Group feedback in seminars
Pre-requisites
Students must have studied the material in CS260 or studied equivalent relevant pre-requisite material.
Courses
This module is Core for:
- Year 3 of UCSA-G4G1 Undergraduate Discrete Mathematics
- Year 3 of UCSA-G4G3 Undergraduate Discrete Mathematics
- Year 4 of UCSA-G4G4 Undergraduate Discrete Mathematics (with Intercalated Year)
- Year 4 of UCSA-G4G2 Undergraduate Discrete Mathematics with Intercalated Year
This module is Optional for:
- Year 4 of UMAA-G105 Undergraduate Master of Mathematics (with Intercalated Year)
- Year 4 of USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
-
USTA-G1G4 Undergraduate Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
- Year 4 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
- Year 5 of G1G4 Mathematics and Statistics (BSc MMathStat) (with Intercalated Year)
This module is Option list A for:
- Year 4 of UCSA-G504 MEng Computer Science (with intercalated year)
- Year 3 of UCSA-G500 Undergraduate Computer Science
- Year 4 of UCSA-G502 Undergraduate Computer Science (with Intercalated Year)
-
UCSA-G503 Undergraduate Computer Science MEng
- Year 3 of G500 Computer Science
- Year 3 of G503 Computer Science MEng
- Year 3 of USTA-G302 Undergraduate Data Science
- Year 3 of USTA-G304 Undergraduate Data Science (MSci)
- Year 4 of USTA-G303 Undergraduate Data Science (with Intercalated Year)
This module is Option list B for:
-
UMAA-G105 Undergraduate Master of Mathematics (with Intercalated Year)
- Year 4 of G105 Mathematics (MMath) with Intercalated Year
- Year 5 of G105 Mathematics (MMath) with Intercalated Year
- Year 3 of UMAA-G100 Undergraduate Mathematics (BSc)
-
UMAA-G103 Undergraduate Mathematics (MMath)
- Year 3 of G100 Mathematics
- Year 3 of G103 Mathematics (MMath)
- Year 4 of G103 Mathematics (MMath)
- Year 4 of UMAA-G107 Undergraduate Mathematics (MMath) with Study Abroad
-
UMAA-G106 Undergraduate Mathematics (MMath) with Study in Europe
- Year 3 of G106 Mathematics (MMath) with Study in Europe
- Year 4 of G106 Mathematics (MMath) with Study in Europe
- Year 3 of USTA-GG14 Undergraduate Mathematics and Statistics (BSc)
- Year 4 of USTA-GG17 Undergraduate Mathematics and Statistics (with Intercalated Year)
- Year 4 of UMAA-G101 Undergraduate Mathematics with Intercalated Year
This module is Option list D for:
- Year 3 of USTA-G1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)