Logo ČVUT
CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

Algorithms and Graphs 2

The course is not on the list Without time-table
Code Completion Credits Range Language
BI-AG2 Z,ZK 5 2P+2C Czech

Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Theoretical Computer Science
Synopsis:

This course, presented in Czech, introduces basic algorithms and concepts of graph theory as a follow=up on the introduction given in the compulsory course BI-AG1. It further delves into advances data structures and amortized complexity analysis. It also includes a very light introduction to approximation algorithms.

For English version of the course see BIE-AG2.

Requirements:

Knowledge of graph theory, graph algorithms, data structures, and amortized analysis in scope of BI-AG1 is assumed. In some lectures we further make use of basic knowledge from BI-ZMA, BI-LIN, or BI-ZDM.

Syllabus of lectures:

1. Havel's theorem, DFS tree, 2-connectivity, an algorithm for finding bridges.

2. Finding strongly connected components, characterization of 2-connected graphs.

3. Networks, flows in networks, Ford-Fulkerson algorithm.

4. k-Connectivity, Ford-Fulkerson theorem, Menger's theorem.

5. Matching, finding matching in bipartite graphs, Hall's theorem and its corollaries.

6. Planar graphs, planar drawing, Euler's formula and its corollaries, Kuratowski's theorem.

7. Dual of a plane graph, multigraphs, graph coloring, first-fit algorithm, Five Color theorem, Mycielski's construction.

8. Finding all-pairs distance, Floyd-Warshall algorithm, using Dijkstra's algorithm.

9. Fibonacci heaps.

10. (a,b)-trees, B-trees, universal hashing.

11. Eulerian graphs, cycle space of a graph.

12. Hamiltonian graphs, Traveling Salesperson problem, approximation algorithms.

13. Algorithms of computational geometry, convex envelope, sweep-line.

Syllabus of tutorials:

1. Renewal of knowledge from BIE-AG1

2. Havel's theorem, DFS tree, 2-connectivity, an algorithm for finding bridges.

3. Finding strongly connected components, characterization of bipartite graphs.

4. Networks, flows in networks, Ford-Fulkerson algorithm.

5. k-Connectivity, Ford-Fulkerson theorem, Menger's theorem.

6. Matching, finding matching in bipartite graphs, Hall's theorem and its corollaries.

7. Planar graphs, planar drawing, Euler's formula and its corollaries, Kuratowski's theorem.

8. Dual of a plane graph, multigraphs, graph coloring, first-fit algorithm, Five Color theorem, Mycielski's construction.

9. Finding all-pairs distance, Floyd-Warshall algorithm, using Dijkstra's algorithm, Fibonacci heaps.

10. semestral test

11. (a,b)-trees, B-trees, universal hashing, Eulerian graphs, cycle space of a graph.

12. Hamiltonian graphs, Traveling Salesperson problem, approximation algorithms.

Study Objective:

The goals of the study are to get familiar with the most basic terms and relations of the Graph Theory, graph algorithms and data structures, which were not part of the BIE-AG1.21 course. Another goal is to understand more complex amortized analysis and to gain basic knowledge of approximation and geometric algorithms.

Study materials:

[1] M. Mareš, T. Valla: Průvodce labyrintem algoritmů, CZ.NIC, Praha, 2017. https://knihy.nic.cz/

[2] T. Valla, J. Matoušek: Kombinatoriky a grafy I., Skripta, KAM MFF UK, Praha, 2008.

[3] P. Kovář: Teorie grafů, učební text, 2016.

[4] J. Matoušek, J. Nešetřil: Kapitoly z diskrétní matematiky, čtvrté vydání, Karolinum, 2010.

[5] J. Kolář: Teoretická Informatika, Česká informatická společnost, Praha, 2004.

[6] J. Demel: Grafy a jejich aplikace, vlastním vydáním, Praha, 2015.

[7] P. Hliněný: Základy Teorie Grafů pro (nejen) informatiky, skripta FI MU, Brno, 2010.

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

[9] K. Mehlhorn, P. Sanders: Algorithms and Data Structures: The Basic Toolbox, Springer Berlin Heidelberg, 2008.

[10] D. B. West: Introduction to Graph Theory, Second edition, Prentice Hall, 2001.

[11] R. Diestel: Graph Theory, 5th edition, Springer-Verlag, Berlin, 2017.

Note:
Further information:
https://courses.fit.cvut.cz/BI-AG2/
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2023-11-30
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet3458206.html