CM30073: Advanced algorithms & complexity
[Page last updated: 09 August 2024]
| Academic Year: | 2024/25 |
| Owning Department/School: | Department of Computer Science |
| Credits: | 6 [equivalent to 12 CATS credits] |
| Notional Study Hours: | 120 |
| Level: | Honours (FHEQ level 6) |
| Period: |
- Semester 2
|
| Assessment Summary: | EX 100% |
| Assessment Detail: | |
| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
|
| Requisites: |
Before taking this module you must take CM10227 AND take CM20217
|
| Learning Outcomes: |
1. To be able to recognise NP-hard problems and prove the appropriate reductions.
2. To cope with NP-complete problems.
3. To know some fundamental methods of proving lower complexity bounds.
|
| Aims: | To present a detailed introduction to one of the central concepts of combinatorial algorithmics: NP-completeness; to extend this concept to real numbers computations; to study foundations of a more general problem of proving lower complexity bounds.
|
| Skills: | Applications of Number (IT).
|
| Content: | NP-completeness: Deterministic and Non-deterministic Turing Machines; class NP; versions of reducibility; NP-hard and NPcomplete problems. Proof of NP-completeness of satisfiability problem for Boolean formulae.
Other NP-complete problems: clique, vertex cover, travelling salesman, subgraph isomorphism, etc. Polynomial-time approximation algorithms for travelling salesman and some otherNP-complete graph problems.
Real Number Turing machines: Definitions; completeness of real roots existence problem for 4-degree polynomials.
Lower complexity bounds: Algebraic computation trees and their complexities; complexity of distinctness problem and of knapsack.
|
| Course availability: |
CM30073 is Optional on the following courses:
Department of Computer Science
- USCM-AFB06 : BSc(Hons) Computer Science (Year 3)
- USCM-AAB07 : BSc(Hons) Computer Science with Study year abroad (Year 4)
- USCM-AKB07 : BSc(Hons) Computer Science with Year long work placement (Year 4)
- USCM-AFB27 : BSc(Hons) Computer Science and Artificial Intelligence (Year 3)
- USCM-AAB27 : BSc(Hons) Computer Science and Artificial Intelligence with Study year abroad (Year 4)
- USCM-AKB27 : BSc(Hons) Computer Science and Artificial Intelligence with Year long work placement (Year 4)
- USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 3)
- USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
- USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
- USCM-AFM01 : MComp(Hons) Computer Science (Year 3)
- USCM-AAM02 : MComp(Hons) Computer Science with Study year abroad (Year 3)
- USCM-AKM02 : MComp(Hons) Computer Science with Year long work placement (Year 3)
- USCM-AFM27 : MComp(Hons) Computer Science and Artificial Intelligence (Year 3)
- USCM-AAM27 : MComp(Hons) Computer Science and Artificial Intelligence with Study year abroad (Year 3)
- USCM-AKM27 : MComp(Hons) Computer Science and Artificial Intelligence with Year long work placement (Year 3)
- USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
- USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 3)
- USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 3)
|
Notes: - This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
- Courses and units are subject to change in accordance with normal University procedures.
- Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
- Find out more about these and other important University terms and conditions here.
|
