Module Details

The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title Complexity of Algorithms
Code COMP202
Coordinator Professor PJ Krysta
Computer Science
P.Krysta@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2021-22 Level 5 FHEQ Second Semester 15

Aims

To demonstrate how the study of algorithmics has been applied in a number of different domains. To introduce formal concepts of measures of complexity and algorithms analysis. To introduce fundamental methods in data structures and algorithms design. To make students aware of computationally hard problems and possible ways of coping with them.


Learning Outcomes

(LO1) At the conclusion of the module students should have an appreciation of the diversity of computational fields to which algorithmics has made significant contributions.

(LO2) At the conclusion of the module students should  have fluency in using basic data structures (queues, stacks, trees, graphs, etc) in conjunction with classical algorithmic problems (searching, sorting, graph algorithms, security issues) and be aware of basic number theory applications, etc.

(LO3) At the conclusion of the module students should  be familiar with formal theories providing evidence that many important computational problems are inherently intractable, e.g., NP-completeness.


Syllabus

 

1 A) Efficiency of Algorithms and Complexity Measures Examples of algorithmic problems and introduction of complexity measures in terms of various resources (time, space, power consumption, number of exchanged messages, etc).  (1 lecture)  Asymptotic complexity and notation in conjunction with a discussion on the worst-case versus the average-case complexity. Also recurrence equations and master method. (2 lectures).  B)   Algorithms and Data Structures  Introduction and analysis of basic data structures with their efficient implementation, including: stack (array), queue (cyclic buffer), and priority queue (heap). (3 lectures) Rooted trees - efficient data structures with implementation, from: tree traversal, binary search trees, balanced trees – AVL and 2-3 trees, Graphs and their implementations. (4 lectures) Advanced graph algorithms, including: network flow algorithms and bipartite matchings. (5 lectures)  Elementary number theory, Euclid’s GCD algorithm, cryptography (from: symmetric encryption, public-key cryptosystem, RSA). (4 lectures) Greedy algorithms and divide-and-conquer algorithms, dynamic programming (8 lectures) Text processing, including pattern matching (from: Knuth-Morris-Pratt, Boyer-Moore, Rabin-Karp), longest common subsequence (dynamic programming). (3 lectures)  C)   Computational Intractability and NP-Completeness   Introduction:  Comparison of two ‘similar’ problems (Euler and Hamiltonian cycle);  other example problems:  3-Colouring, Satisfiability, k-Clique, etc;  Common features of the problems. (1 lecture)  TheComplexity Class NP:  formulation of computational problems in terms of questions about witnesses to solutions; completeness; background to Cook’s Theorem and its significance, intuitions behind Cook’s Theorem (2 lectures) Selected standard reductions:  SAT to 3-SAT, SAT to Clique ( 1 lecture)


Teaching and Learning Strategies

Teaching Method 1 - Lecture
Description:
Teaching Method 2 - Tutorial
Description:

Due to Covid-19, in 2021/22, one or more of the following delivery methods will be implemented based on the current local conditions.
(a) Hybrid delivery
Teaching Method 1 - Lecture
Description: Mix of on-campus/on-line synchronous/asynchronous sessions
Teaching Method 2 - Tutorial
Description: Mix of on-campus/on-line synchronous/asynchronous sessions

(b) Fully online delivery and assessment
Teaching Method 1 - Lecture
Description: On-line synchronous/asynchronous lectures
Teaching Method 2 - Tutorial
Description: On-line synchronous/asynchronous sessions

(c) Standard on-campus delivery
Teaching Method 1 - Lecture
Description: Mix of on-campus/on-line synchronous/asynchronous sessions
Teaching Method 2 - Tutorial
Description: On-campus synchronous sessions


Teaching Schedule

  Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
Study Hours 36

    12

    48
Timetable (if known)              
Private Study 102
TOTAL HOURS 150

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
(202) Written Exam There is a resit opportunity: Resit exam will replace failed CA components, the Learning Outcomes will be covered in the resit exam. Standard UoL penalty applies for late submis  120 minutes.    70       
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
(202.1) Class Test There is a resit opportunity: Resit exam will replace failed CA components, the Learning Outcomes will be covered in the resit exam. Standard UoL penalty applies for late submiss  1 hours    15       
(202.2) Programming Assignment There is a resit opportunity: Resit exam will replace failed CA components, the Learning Outcomes will be covered in the resit exam. Standard UoL penalty applies for   3 hours    15       

Recommended Texts

Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.