Algorithms and Graphs 1
Code  Completion  Credits  Range  Language 

BIEAG1  Z,ZK  6  2P+2C  English 
 Vztahy:
 It is not possible to register for the course BIEAG1 if the student is concurrently registered for or has already completed the course BIEAX1 (mutually exclusive courses).
 Garant předmětu:
 Lecturer:
 Tutor:
 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 BIEAAG and BIEZDM 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:

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 BIEAAG and BIEZDM.
 Syllabus of lectures:

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 edgelabelled graphs. Jarník’s algorithm and Kruskal’s algorithm and their implementations.
12. [2] Shortest paths algorithms on edgelabelled 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, 9780262033848,
[2] Gibbons, A.: Algorithmic Graph Theory, Cambridge University Press, 1985, 9780521288811,
[3] Gross, J. L.  Yellen, J.  Zhang, P.: Handbook of Graph Theory, 2nd Edition (Discrete Mathematics and Its Applications), Chapman and Hall/CRC, 2013, 9781439880180,
 Note:
 Further information:
 https://courses.fit.cvut.cz/BIEAG1/
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Bachelor branch Security and Information Technology, in English, 20152020 (compulsory course in the program)
 Bachelor branch Web and Software Engineering, spec. Software Engineering, in English, 20152020 (compulsory course in the program)
 Bachelor branch Computer Science, in English, 20152020 (compulsory course in the program)