Algorithms and Graphs 2

The course is not on the list Without time-table

Code	Completion	Credits	Range	Language
BIE-AG2.21	Z,ZK	5	2P+2C	English

It is not possible to register for the course BIE-AG2.21 if the student is concurrently registered for or has already completed the course BIE-AX2 (mutually exclusive courses).

It is not possible to register for the course BIE-AG2.21 if the student is concurrently registered for or has previously completed the course BIE-AX2 (mutually exclusive courses).

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Theoretical Computer Science

Synopsis:

The course presents the basic algorithms and concepts of graph theory building on the introduction exposed in the compulsory course BIE-AG1.21. It also covers advanced data structures and amortized analysis. It also includes a very light introduction into approximation algorithms.

Requirements:

Knowledge of graph theory, graph algorithms, data structures, and amortized analysis in scope of BIE-AG1.21 is assumed. In some lectures we further make use of basic knowledge from BIE-MA1.21, BIE-LA1.21, or BIE-DML.21.

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. Diestel R. : Graph Theory (5th Edition). Springer, 2017. ISBN 978-3-662-53621-6.

2. West D. B. : Introduction to Graph Theory (2nd Edition). Prentice-Hall, 2001. ISBN 978-0130144003.

3. Cormen T. H., Leiserson C. E., Rivest R. L., Stein C. : Introduction to Algorithms (3rd Edition). MIT Press, 2016. ISBN 978-0262033848.

Note:

Further information:

https://courses.fit.cvut.cz/BIE-AG2/

No time-table has been prepared for this course

The course is a part of the following study plans: