After successful completion of the course, students are able to...

- design algorithms that use the decompositions associated with parameters such as treewidth, clique-width, and hypertree-width to solve problems efficiently.

- represent problems in artificial intelligence and database theory using different graph models (primal graph, incidence graph, hypergraph).

- prove upper and lower bounds for (some) width parameters in simple cases.

Many combinatorial problems that are intractable in general can be efficiently solved on tree-like structures. Width parameters measuring "tree-likeness" and their corresponding decompositions can be used to design algorithms that are fast as long as the width of the input is reasonably small.

The course will cover common graph and hypergraph width parameters and some of their applications in AI and database theory. Specifically, we will discuss the graph measure tree-width and generalizations such as clique-width and rank-width. We then proceed to discuss hypergraph width parameters like hypertree-width and fractional hypertree-width.

We will also showcase applications of width parameters to problems such as propositional model counting, conjunctive query evaluation, and inference in Bayesian Networks.

Students solve exercise sheets based on pre-recorded video lectures. Solutions are subsequently presented and discussed during live video calls.

ECTS Breakdown:

20 h video lectures and readings
45 h solving exercise sheets
10 h presentation of exercises
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75 h total

Grading is based on the number of solved exercises and their presentation.

- Jörg Flum, Martin Grohe: Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series, Springer 2006.

- Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, Saket Saurabh: Parameterized Algorithms. Springer 2015.

This course requires familiarity with fundamental graph theoretic definitions as well as basic knowledge of algorithmics and complexity theory. Knowledge of the topics covered in the "Algorithmics" course is an advantage.