Algorithms and Graphs 1

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Theoretical Computer Science

Synopsis:

The course covers the basics of efficient algorithm design, data structures, and graph theory, belonging to the core knowledge of every computing curriculum.

It links and partially develops the knowledge from the course BI-DML.21, in which students acquire the knowledge and skills in combinatorics necessary for evaluating the time and space complexity of algorithms. The course also follows up knowledge from BI-MA1.21, the practical usage of asymptotic mathematics, in particular, the asymptotic notation.

Requirements:

Active algorithmic skills for solving basic types of computational tasks, C++ programming skills, and knowledge of basic notions from mathematical analysis and combinatorics are expected. Students should take the concurrent course BIE-AAG.21.

Syllabus of lectures:

1. Motivation and Elements of Graph Theory.

2. Basic Definitions and Elements of Graph Theory I.

3. Basic Definitions and Elements of Graph Theory II.

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

5. Extendable Array, Amortized Complexity, Binomial Heaps.

6. Search Trees and Balance Strategies.

7. Introduction to Randomization, Hashing.

8. Recursive algorithm and the Divide-and-Conquer method.

9. Probabilistic Algorithms and Their Complexity. QuickSort.

10. Dynamic Programming.

11. Minimum Spanning Trees.

12. Shortest Paths Algorithms on Graphs.

Syllabus of tutorials:

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.

Study Objective:

Study materials:

[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,

Note:

Further information:

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

No time-table has been prepared for this course

The course is a part of the following study plans:

• Bachelor program Informatics, unspecified branch, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Security and Information Technology, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Computer Science, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Computer Engineering, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Information Systems and Management, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Web and Software Engineering, spec. Software Engineering, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Web and Software Engineering, spec. Web Engineering, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Web and Software Engineering, spec. Computer Graphics, in Czech, 2015-2020 (compulsory course in the program)
• Bachelor branch Knowledge Engineering, in Czech, 2018-2020 (compulsory course in the program)