Algorithms and Graphs 1

Předmět BIE-AG1 nesmí být zapsán, je-li v témže semestru zapsán anebo již dříve absolvován předmět BIE-AX1 (vztah je symetrický)

Garant předmětu:

Přednášející:

Cvičící:

Předmět zajišťuje:

katedra teoretické informatiky

Anotace:

The course covers the basics from the efficient algorithm design, data structures, and graph theory, belonging to the core knowledge of every computing curriculum. It is interlinked with the concurrent BIE-AAG and BIE-ZDM courses in which the students gain the basic skills and knowledge needed for time and space complexity of algorithms and learn to handle practically the asymptotic mathematics.

Požadavky:

Active algorithmic skills for solving basic types of computational tasks, programming skills in some HLL (Java, C++), and knowledge of basic notions from the mathematical analysis and combinatorics are expected. Students are expected to take concurrent courses BIE-AAG and BIE-ZDM.

Osnova přednášek:

1. Motivation, graph definition, important types of graphs, undirected graphs, graph representation, subgraphs.

2. Connectivity, connected components, DFS, directed graphs, trees.

3. Spanning trees, distances in graphs, BFS, topological ordering.

4. Basic sorting algorithms with the quadratic time complexity. Binary heap as a partial ordered structure, HeapSort.

5. Extendable array, amortized complexity. Binomial Heaps.

6. Operations and properties of binary search trees, balancing strategies, AVL trees.

7. Randomized algorithms. Introduction to probability theory. Hash tables and strategies of collision resolving.

8. Recursive algorithms and Divide and Conquer algorithms.

9. QuickSort. Lower bound of complexity for sorting problem in the comparison model. Special sorting algorithms.

10. Dynamic programming.

11. Minimum spanning trees of edge-labelled graphs. Jarník’s algorithm and Kruskal’s algorithm and their implementations.

12. [2] Shortest paths algorithms on edge-labelled graphs.

Osnova cvičení:

1. Motivation and Elements of Graph Theory I.

2. Elements of Graph Theory II.

3. Elements of Graph Theory III. 1st ProgTest.

4. Sorting Algorithms O(n^2). Binary Heaps.

5. Extendable Array, Amortized Complexity, Binomial Heaps.

6. Search Trees and Balance Strategies. 2nd ProgTest.

7. Hashing and Hash tables.

8. Recursive Algorithms and Divide et Impera Method.

9. Probabilistic Algorithms and their Complexity. QuickSort.

10. Semestral test.

11. Dynamic Programming. 3rd ProgTest.

13. Minimum Spanning Trees, Shortest Paths.

Cíle studia:

Studijní materiály:

[1] Cormen, T. H. - Leiserson, C. E. - Rivest, R. L. - Stein, C.: Introduction to Algorithms, 3rd Edition, MIT Press, 2009, 978-0262033848,

[2] Gibbons, A.: Algorithmic Graph Theory, Cambridge University Press, 1985, 978-0521288811,

[3] Gross, J. L. - Yellen, J. - Zhang, P.: Handbook of Graph Theory, 2nd Edition (Discrete Mathematics and Its Applications), Chapman and Hall/CRC, 2013, 978-1439880180,

Poznámka:

Information about the course and courseware are available at https://courses.fit.cvut.cz/BIE-AG1/

Další informace:

https://courses.fit.cvut.cz/BIE-AG1/

Pro tento předmět se rozvrh nepřipravuje

Předmět je součástí následujících studijních plánů:

• Bachelor branch Security and Information Technology, in English, 2015-2020 (povinný předmět programu)
• Bachelor branch Web and Software Engineering, spec. Software Engineering, in English, 2015-2020 (povinný předmět programu)
• Bachelor branch Computer Science, in English, 2015-2020 (povinný předmět programu)