186.856 Structural Decompositions and Algorithms
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2023S, VU, 2.0h, 3.0EC


  • Semester hours: 2.0
  • Credits: 3.0
  • Type: VU Lecture and Exercise
  • Format: Hybrid

Learning outcomes

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.

Subject of course

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.

Teaching methods

Students solve exercise sheets based on lectures. Solutions are subsequently presented and discussed in exercise classes.

Mode of examination


Additional information

ECTS Breakdown:

20 h lectures (videos for online participants) and readings
45 h solving exercise sheets
10 h presentation of exercises
75 h total


  • Slivovsky, Friedrich


Course dates

Tue14:00 - 16:0014.03.2023 - 27.06.2023Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Structural Decompositions and Algorithms - Single appointments
Tue14.03.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue21.03.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue28.03.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue18.04.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue25.04.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue02.05.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue09.05.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue16.05.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue23.05.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue06.06.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue13.06.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue20.06.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture
Tue27.06.202314:00 - 16:00Seminarraum FAV 01 C (Seminarraum 188/2) Lecture

Examination modalities

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

Course registration

Begin End Deregistration end
08.02.2023 00:00 29.04.2023 00:00 29.04.2023 00:00


Study CodeObligationSemesterPrecon.Info
066 645 Data Science Not specified
066 646 Computational Science and Engineering Not specified
066 926 Business Informatics Not specified
066 931 Logic and Computation Not specified
066 937 Software Engineering & Internet Computing Not specified
066 938 Computer Engineering Mandatory elective


- 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.

Previous knowledge

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.

Preceding courses