Description:

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.

Contents:

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.

Seminar contents:

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.

Recommended literature:

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.

Keywords:

Graph Theory, Graph Algorithms, Data Structures, Approximation Algorithm, Geometry Algorithms

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar