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CM30073: Advanced algorithms & complexity

Academic Year: 2018/9
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:
  • Examination (EX 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must ( take CM10227 OR take XX10190 ) AND ( take 2 MODULES FROM {CM10196, CM20217} OR take MA10209 )
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. 		Before taking this module you must ( take CM10227 OR take XX10190 ) AND ( take CM10196 OR take MA10209 ) AND take CM20217
Programme availability:

CM30073 is Optional on the following programmes:

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-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-AFB09 : BSc(Hons) Computer Science with Business (Year 3)
  • USCM-AAB10 : BSc(Hons) Computer Science with Business with Study year abroad (Year 4)
  • USCM-AKB10 : BSc(Hons) Computer Science with Business 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 4)
  • USCM-AKM02 : MComp(Hons) Computer Science with Year long work placement (Year 4)
  • USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
  • USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
  • USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
Department of Mathematical Sciences
  • TSMA-AFM08 : MSc Modern Applications of Mathematics
  • TSMA-AWM14 : MSc Modern Applications of Mathematics
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
  • USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
  • USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AFB05 : BSc(Hons) Statistics (Year 3)
  • USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
  • USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

Notes:

  • This unit catalogue is applicable for the 2018/19 academic year only. Students continuing their studies into 2019/20 and beyond should not assume that this unit will be available in future years in the format displayed here for 2018/19.
  • Programmes 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.
  • Undergraduates: .
  • Postgraduates: .