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.
BI-AG2 Algorithms and Graphs 2 Extent of teaching: 2P+2C Instructor: Completion: Z,ZK Department: 18101 Credits: 5 Semester: L Annotation:
This course, presented in Czech, introduces basic algorithms and concepts of graph theory as a follow=up on the introduction given in the compulsory course BI-AG1. It further delves into advances data structures and amortized complexity analysis. It also includes a very light introduction to approximation algorithms. For English version of the course see BIE-AG2.
Lecture syllabus:
1. Havel's theorem, DFS tree, 2-connectivity, an algorithm for finding bridges. 2. Finding strongly connected components, characterization of 2-connected graphs. 3. Networks, flows in networks, Ford-Fulkerson algorithm. 4. k-Connectivity, Ford-Fulkerson theorem, Menger's theorem. 5. Matching, finding matching in bipartite graphs, Hall's theorem and its corollaries. 6. Planar graphs, planar drawing, Euler's formula and its corollaries, Kuratowski's theorem. 7. Dual of a plane graph, multigraphs, graph coloring, first-fit algorithm, Five Color theorem, Mycielski's construction. 8. Finding all-pairs distance, Floyd-Warshall algorithm, using Dijkstra's algorithm. 9. Fibonacci heaps. 10. (a,b)-trees, B-trees, universal hashing. 11. Eulerian graphs, cycle space of a graph. 12. Hamiltonian graphs, Traveling Salesperson problem, approximation algorithms. 13. Algorithms of computational geometry, convex envelope, sweep-line. Seminar syllabus:
1. Renewal of knowledge from BIE-AG1 2. Havel's theorem, DFS tree, 2-connectivity, an algorithm for finding bridges. 3. Finding strongly connected components, characterization of bipartite graphs. 4. Networks, flows in networks, Ford-Fulkerson algorithm. 5. k-Connectivity, Ford-Fulkerson theorem, Menger's theorem. 6. Matching, finding matching in bipartite graphs, Hall's theorem and its corollaries. 7. Planar graphs, planar drawing, Euler's formula and its corollaries, Kuratowski's theorem. 8. Dual of a plane graph, multigraphs, graph coloring, first-fit algorithm, Five Color theorem, Mycielski's construction. 9. Finding all-pairs distance, Floyd-Warshall algorithm, using Dijkstra's algorithm, Fibonacci heaps. 10. semestral test 11. (a,b)-trees, B-trees, universal hashing, Eulerian graphs, cycle space of a graph. 12. Hamiltonian graphs, Traveling Salesperson problem, approximation algorithms. Literature:
[1] M. Mareš, T. Valla: Průvodce labyrintem algoritmů, CZ.NIC, Praha, 2017. https://knihy.nic.cz/ [2] T. Valla, J. Matoušek: Kombinatoriky a grafy I., Skripta, KAM MFF UK, Praha, 2008. [3] P. Kovář: Teorie grafů, učební text, 2016. [4] J. Matoušek, J. Nešetřil: Kapitoly z diskrétní matematiky, čtvrté vydání, Karolinum, 2010. [5] J. Kolář: Teoretická Informatika, Česká informatická společnost, Praha, 2004. [6] J. Demel: Grafy a jejich aplikace, vlastním vydáním, Praha, 2015. [7] P. Hliněný: Základy Teorie Grafů pro (nejen) informatiky, skripta FI MU, Brno, 2010. [8] Cormen, T. H. - Leiserson, C. E. - Rivest, R. L. - Stein, C.: Introduction to Algorithms, 3rd Edition, MIT Press, 2009. [9] K. Mehlhorn, P. Sanders: Algorithms and Data Structures: The Basic Toolbox, Springer Berlin Heidelberg, 2008. [10] D. B. West: Introduction to Graph Theory, Second edition, Prentice Hall, 2001. [11] R. Diestel: Graph Theory, 5th edition, Springer-Verlag, Berlin, 2017. Requirements:
Knowledge of graph theory, graph algorithms, data structures, and amortized analysis in scope of BI-AG1 is assumed. In some lectures we further make use of basic knowledge from BI-ZMA, BI-LIN, or BI-ZDM.
Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/BI-AG2/ The course is also part of the following Study plans:
Page updated 23. 4. 2024, semester: Z/2024-5, Z,L/2022-3, Z/2019-20, Z,L/2021-2, Z,L/2023-4, L/2019-20, Z,L/2020-1, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška