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.
BIE-AG2.21 Algorithms and Graphs 2 Extent of teaching: 2P+2C Instructor: Suchý O. Completion: Z,ZK Department: 18101 Credits: 5 Semester: L Annotation:
The course presents the basic algorithms and concepts of graph theory building on the introduction exposed in the compulsory course BIE-AG1.21. It also covers advanced data structures and amortized analysis. It also includes a very light introduction into approximation algorithms.
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. Diestel R. : Graph Theory (5th Edition). Springer, 2017. ISBN 978-3-662-53621-6. 2. West D. B. : Introduction to Graph Theory (2nd Edition). Prentice-Hall, 2001. ISBN 978-0130144003. 3. Cormen T. H., Leiserson C. E., Rivest R. L., Stein C. : Introduction to Algorithms (3rd Edition). MIT Press, 2016. ISBN 978-0262033848. Requirements:
Knowledge of graph theory, graph algorithms, data structures, and amortized analysis in scope of BIE-AG1.21 is assumed. In some lectures we further make use of basic knowledge from BIE-MA1.21, BIE-LA1.21, or BIE-DML.21.
Information and materials for the course can be found at https://courses.fit.cvut.cz/BIE-AG2/ The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester BIE-TI.21 Computer Science 2021 PS 4 BIE-PS.21 Computer Networks and Internet 2021 VO 4
Page updated 19. 4. 2024, semester: L/2020-1, L/2021-2, Z/2023-4, Z/2024-5, Z/2019-20, Z/2022-3, L/2019-20, L/2022-3, Z/2020-1, Z/2021-2, L/2023-4, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška