Algorithms and Graphs 2

Vztahy:

Předmět BIE-AG2.21 nesmí být zapsán, je-li v témže semestru zapsán anebo již dříve absolvován předmět BIE-AX2 (vztah je symetrický)

Předmět BIE-AG2.21 nesmí být zapsán, je-li v témže semestru zapsán anebo již dříve absolvován předmět BIE-AX2 (vztah je symetrický)

Předmět je ekvivalentní s BI-AG2,BI-AG2.21,BIE-AG2 .

Garant předmětu:

Ondřej Suchý

Přednášející:

Ondřej Suchý

Cvičící:

Jiřina Scholtzová

Předmět zajišťuje:

katedra teoretické informatiky

Anotace:

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.

Požadavky:

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.

Osnova přednášek:

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.

Osnova cvičení:

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.

Cíle studia:

The goals of the study are to get familiar with the most basic terms and relations of the Graph Theory, graph algorithms and data structures, which were not part of the BIE-AG1.21 course. Another goal is to understand more complex amortized analysis and to gain basic knowledge of approximation and geometric algorithms.

Studijní materiály:

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.

Poznámka:

Information and materials for the course can be found at https://courses.fit.cvut.cz/BIE-AG2/

Další informace:

https://courses.fit.cvut.cz/BIE-AG2/

Rozvrh na zimní semestr 2024/2025:

Rozvrh není připraven

Rozvrh na letní semestr 2024/2025:

Rozvrh není připraven

Předmět je součástí následujících studijních plánů:

• Bachelor Specialization, Computer Science, 2021 (PS)
• Bachelor Specialization, Computer Networks and Internet, 2021 (VO)