Main page | Study Branches/Specializations | Groups of Courses | All Courses | Roles                Instructions

A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

NI-CPX Complexity Theory Extent of teaching: 3P+1C
Instructor: Knop D., Suchý O. Completion: Z,ZK
Department: 18101 Credits: 5 Semester: Z

Annotation:
Students will learn about the fundamental classes of problems in the complexity theory and different models of algoritms and about implications of the theory concerning practical (in)tractability of difficult problems.

Lecture syllabus:
1. Computational problems and models of computation
2. Undecideability, non-determinism, class NP, existence of an NP-complete problem
3. Further NP-complete problems, strong and weak NP-hardness, pseudopolynomial algorithms
4. Classes coNP and NP intersection coNP, polynomial hierarchy
5. Problem of P=NP, relativization
6. Class PSPACE, Savitch's Theorem
7. PSPACE-complete problems (quantified formulas and games), problems hard for classes of the hierarchy
8. Logspace
9. Circuit complexity, P/poly, circuits of bounded depth, paralelization of computation
10. P-completeness
11. Randomized algorithms
12. Relations between classes of randomized algorithms and with other classes
13. Optimalization probléms, Approximation algorithms
14. Probabilistically checkable proof, gap problem, PCP theorem
15. Communication complexity
16. Complexity of counting, #P
17. (Strong) Exponential Time Hypothesis, corollaries
18. Pseudo random number generators, derandomization

Seminar syllabus:
1. Complexity of algorithms, simulation of models of computation in different model
2. Problems outside NP, various NP-complete problems a reductions between them, problems in coNP
3. Problems in PSPACE and various classes of the polynomial hierarchy, examples of circuits for various simple problems
4. Various approximation algorithms a proofs of inapproximability
5. Amplification of success probability of randomized algorithms, examples of randomized algorithms
6. Communication schemes, lower bounds for communication complexity

Literature:
S. Arora, B. Barak, ''Computational Complexity: A Modern Approach''. Cambridge University Press, 2009. ISBN 0521424267.
Christos H. Papadimitriou, ?Computational Complexity?. Pearson, 1993. ISBN 978-0201530827
D. P. Williamson, D. B. Shmoys: ?The Design of Approximation Algorithms?, Cambridge university press, 2011. ISBN 9780521195270
V. V. Vazirani: Approximation Algorithms, Springer, 2001. ISBN 3540653678
R. Motwani, P. Raghavan, ''Randomized Algorithms''. Cambridge University Press, 1995. ISBN 0521474655.

Requirements:
Knowledge of graph theory and graph algorithms in scope of BIE-AG1, as well as formal languages, Turing machines, P and NP classes, and nedeterminism in scope of BIE-AAG is assumed. Knowledge from BIE-AG2, such as Hamilton cycles, TSP, approximation algorithms, etc. is highly beneficial.

Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/MI-CPX/

The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
NI-PB.2020 Computer Security V 3
NI-ZI.2020 Knowledge Engineering V 3
NI-SPOL.2020 Unspecified Branch/Specialisation of Study V 3
NI-TI.2020 Computer Science V 3
NI-TI.2023 Computer Science V 3
NI-NPVS.2020 Design and Programming of Embedded Systems V 3
NI-PSS.2020 Computer Systems and Networks V 3
NI-MI.2020 Managerial Informatics V 3
NI-SI.2020 Software Engineering (in Czech) V 3
NI-SP.2020 System Programming V 3
NI-WI.2020 Web Engineering V 3
NI-SP.2023 System Programming V 3
NI-TI.2023 Computer Science PS Není


Page updated 28. 3. 2024, semester: Z/2023-4, L/2019-20, L/2022-3, Z/2019-20, Z/2022-3, L/2020-1, L/2023-4, Z/2020-1, Z,L/2021-2, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška