Algorithms and Graphs No Implementation

Relations:

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

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

Course guarantor:

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:

basics of combinatorics and discrete math, basics of logic

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-AX1

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed	roomTH:A-s135 Valla T. 12:45–14:15 (lecture parallel1) Thákurova 7 (budova FSv)
Thu	roomT9:346 Scholtzová J. 12:45–14:15 (lecture parallel1 parallel nr.101) Dejvice NBFIT schoolroom
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: