 Credits:
| 6 |
| Level:
| Honours (FHEQ level 6) |
| Period: |
Semester 2
|
| Assessment:
| EX 100% |
| Supplementary Assessment: | CM30073 Mandatory Extra Work (where allowed by programme regulations) |
| Requisites:
| Before taking this unit you must take CM20028 or (take CM10196 and take CM10197 and take CM20217) |
| Description:
| 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.
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.
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.
|
Programme availability:
|
CM30073 is Optional on the following programmes:
Department of Computer Science
- USCM-AFB01 : BSc Computing (Full-time) - Year 3
- USCM-AKB01 : BSc Computing (Full-time with Thick Sandwich Placement) - Year 4
- USCM-AFB06 : BSc (hons) Computer Science (Full-time) - Year 3
- USCM-AKB07 : BSc (hons) Computer Science (Full-time with Thick Sandwich Placement) - Year 4
- USCM-AFB09 : BSc (hons) Computer Science with Business (Full-time) - Year 3
- USCM-AKB10 : BSc (hons) Computer Science with Business (Full-time with Thick Sandwich Placement) - Year 4
- USCM-AAB10 : BSc (hons) Computer Science with Business with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USCM-AKB15 : BSc (hons) Computer Science with French Language (with Industrial Placement) (Full-time with Thick Sandwich Placement) - Year 4
- USCM-AAB15 : BSc (hons) Computer Science with French Language (with Study Year Abroad) (Full-time with Study Year Abroad) - Year 4
- USCM-AKB16 : BSc (hons) Computer Science with German Language (with Industrial Placement) (Full-time with Thick Sandwich Placement) - Year 4
- USCM-AAB16 : BSc (hons) Computer Science with German Language (with Study Year Abroad) (Full-time with Study Year Abroad) - Year 4
- USCM-AFB13 : BSc (hons) Computer Science with Mathematics (Full-time) - Year 3
- USCM-AKB14 : BSc (hons) Computer Science with Mathematics (Full-time with Thick Sandwich Placement) - Year 4
- USCM-AAB14 : BSc (hons) Computer Science with Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USCM-AKB17 : BSc (hons) Computer Science with Spanish Language (with Industrial Placement) (Full-time with Thick Sandwich Placement) - Year 4
- USCM-AAB17 : BSc (hons) Computer Science with Spanish Language (with Study Year Abroad) (Full-time with Study Year Abroad) - Year 4
- USCM-AAB07 : BSc (hons) Computer Science with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USCM-AFM01 : MComp (hons) Computer Science (Full-time) - Year 3
- USCM-AKM02 : MComp (hons) Computer Science (Full-time with Thick Sandwich Placement) - Year 4
- USCM-AAM02 : MComp (hons) Computer Science with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Department of Mathematical Sciences
- USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
- USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
- USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
- USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
- USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time) - Year 1
- TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time) - Year 1
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