Algorithms and Graphs 1

Vztahy:

It is not possible to register for the course BIE-AG1.21 if the student is concurrently registered for or has already completed the course BIE-AX1 (mutually exclusive courses).

It is not possible to register for the course BIE-AG1.21 if the student is concurrently registered for or has previously completed the course BIE-AX1 (mutually exclusive courses).

Garant předmětu:

Dušan Knop

Lecturer:

Tomáš Valla

Tutor:

Dušan Knop, Maria Saumell Mendiola, Jiřina Scholtzová

Supervisor:

Department of Theoretical Computer Science

Synopsis:

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.

Requirements:

Entry knowledge: 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.

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, 2016. ISBN 978-0262033848.

2. Wengrow J. : A Common-Sense Guide to Data Structures and Algorithms: Level Up Your Core Programming Skills (2nd Edition). Pragmatic Bookshelf, 2020. ISBN 978-1680507225.

3. Sedgewick R. : Algorithms (4th Edition). Addison-Wesley, 2011. ISBN 978-0321573513.

4. Deo N. : Graph Theory with Applications to Engineering and Computer Science. Dover Publications, 2016. ISBN 978-048680793.

5. Bickle A. : Fundamentals of Graph Theory. AMS, 2020. ISBN 978-1470453428.

Note:

Further information:

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

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Bachelor specialization, Computer Engineering, 2021 (compulsory course in the program)
• Bachelor specialization, Information Security, 2021 (compulsory course in the program)
• Bachelor specialization, Software Engineering, 2021 (compulsory course in the program)
• Bachelor specialization, Computer Science, 2021 (compulsory course in the program)
• Bachelor specialization, Computer Networks and Internet, 2021 (compulsory course in the program)
• Bachelor specialization Computer Systems and Virtualization, 2021 (compulsory course in the program)