## CM30073: Advanced algorithms & complexity

[Page last updated: 04 August 2021]

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 )
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-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-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 3)
• USCM-AKM02 : MComp(Hons) Computer Science 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)
Department of Mathematical Sciences
• 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 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. 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. Find out more about these and other important University terms and conditions here.