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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

Problems and Algorithms

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Code Completion Credits Range Language
MIE-PAA Z,ZK 5 2P+1R+1C
Lecturer:
Petr Fišer (guarantor)
Tutor:
Petr Fišer (guarantor)
Supervisor:
Department of Digital Design
Synopsis:

Students are able to evaluate discrete problems by complexity and by the purpose of optimisation (on-line tasks, multicriterial optimisation). They understand principles and properties of heuristics and exact algorithms and, therefore, are able to select, apply, and experimentally evaluate a suitable heuristics for a practical problem.

Requirements:

The notion of complexity, asymptotic complexity bounds. Basic graph theory. Programming in any imperative language using queues, stacks, and lists.

Syllabus of lectures:

1. Combinatorial problems and and algorithms, complexity

2. P and NP classes, polynomial hierarchy of problems

3. NPC and NPH problems, Karp reduction, Turing reduction

4. PO, NPO classes, approximation algorithms, classes APX, PTAS, FPTAS

5. Communication and circuit complexity

6. Randomized algorithms. Experimental evaluation

7. Local methods. State space. Simple local heuristics

8. Simulated annealing

9. Simulated evolution - genetic algorithms

10. Simulated evolution - genetic programming

11. Tabu Search

12. Global methods

13. Linear programming - simplex method

Syllabus of tutorials:

1. Introduction, the Knapsack problem

2. Examples of problems, configuration variables

3. Consultation

4. Dynamic programming

5. Consultation

6. Consultation

7. Problem classes P, NP, NPC, NPH

8. Consultation

9. Mid-term test

10. State space

11. Advanced iterative algorithms

12. Consultation

13. Corrective test, assessment

Study Objective:

Many practical tasks are computationally infeasible. Students will learn to distinguish tasks where the complexity grows too fast with the task size from those which are undecidable independently of size. They will learn fast algorithms for exact and, primarily, approximate solution. Some of the more advanced ones are inspired by processes in nature and sometimes referred to as softcomputing. A series of homeworks will lead students from very simple tasks to applications of advanced heuristics on a practical problem.

Study materials:

1. Garey, M. R., Johnson, D. S. ''Computers and Intractability: A Guide to the Theory of NP-Completeness''. W. H. Freeman, 1979. ISBN 0716710455.

2. Ausiello, G., Crescenzi, P., Kann, V., Gambosi, G., Spaccamela, A. M. ''Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties''. Springer, 2003. ISBN 3540654313.

Note:
Further information:
https://moodle.fit.cvut.cz/courses/MIE-PAA/
Time-table for winter semester 2018/2019:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
roomTH:A-1042
Fišer P.
11:00–12:30
(lecture parallel1)
Thákurova 7 (FSv-budova A)
Hlavickova laborka
roomTH:A-942
Fišer P.
16:15–17:45
(lecture parallel1
parallel nr.101)

Thákurova 7 (FSv-budova A)
Fri
Thu
Fri
Time-table for summer semester 2018/2019:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-05-19
For updated information see http://bilakniha.cvut.cz/en/predmet1437706.html