## News

## Exercise sheet #5
The fifth (last) exercise sheet is available here. The deadline is July 18. |

## Exercise sheet #4
The fourth exercise sheet is available here. The deadline is June 27. The next block of three lectures (27.6, 4.7, 11.7) will be on the combinatorial notion of treewidth and its algorithmic applications. |

## No lecture today
As announced in the last lecture, there is no lecture today. The next lecture is on 20.6 (and the next exercise sheet will be handed out on that day). |

## Lecture delayed by 15 minutes
Today (30.5) the lecture will start at 10:30 due to an emergency situation. Thank you for your understanding. |

## Exercise sheet #3
The third exercise sheet is available here. The deadline is May 30. |

## Exercise #3
Exercise #3 will be out next week after the lecture. There will be no exercise sheet today (this week). |

## Exercise sheet #2
The second exercise sheet is available here. The deadline is May 9. |

## Exercise sheet #1
The first exercise sheet is available here. The deadline is April 25. As announced, 50% of all points on the exercise sheets are needed to be admitted to the (oral) exam. |

## Parameterized Algorithms

This course is about designing fast algorithms for NP-hard graph theoretic problems, where the running time depends on multiple parameters of the input. For example, while a database may contain a very large amount of data, the size of the database queries is typically extremely small in comparison. The aim would be to obtain algorithms that have a small dependence on the database size, but possibly a larger dependence on the query size. Such an algorithm would be fast when the queries are small. Similarly, if the goal is to find small solutions in a large graph, then an algorithm with exponential dependence on the size of the solution and polynomial dependence on the size of the graph might be acceptable.

We will see several algorithmic techniques to design fast algorithms for NP-hard problems in this setting, called *Fixed-Parameter Tractable (FPT) algorithms*, as well as an overview of the lower-bound methods. We will also learn about preprocessing or data-reduction algorithms in this setting, called *Kernelization algorithms*, which run in polynomial time and reduce a given instance of a NP-hard problem to an equivalent but much smaller instance.

Some example topics that will be covered during the course:

- Branching, bounded-depth search trees
- Randomization, color coding
- Iterative compression
- Kernelization, sunflower lemma, crown decomposition
- Kernelization lower bounds
- Algebraic methods, inclusion-exclusion
- Representative sets and matroids
- Important cuts
- Treewidth, bidimensionality on planar graphs
- Turing and lossy kernelization

**Format**

Two hours of lectures every week and two hours of tutorials every other week. During the semester, 5 homework exercise sheets will be handed out, to be submitted in one week. **50% of all points on the exercise sheets are needed to be admitted to the (oral) exam.** The solutions of the exercises are discussed in the tutorial sessions (after the deadline).

Lectures: Tuesday, 10:15-12:00

Tutorial: To be decided

First lecture: April 11, 2023

Room: E 1 4 (MPI-INF) 021

**Prerequisites**

Basic knowledge of algorithms, graph theory and probability will be assumed.

Date |
Topic | Material | Reference (see below) | Exercise | Due |
---|---|---|---|---|---|

April 11 | L01: Introduction I | Slides | 1, 3.1, 3.2, 3.3 | ||

April 18 | L02: Introduction II | Slides | 2.1, 2.2.1, 3.5, 5.1, 5.2 | Sheet 1 | April 25 |

April 25 |
L03: Introduction III |
Slides | 6.1, 4.1, 4.2, 4.3.1, 4.4 | ||

May 2 |
L04: Lower Bounds |
Slides | 13.1, 13.2, 13.3, 13.6, 14.1, 14.2, 14.3 | Sheet 2 | May 9 |

May 9 |
L05: Kernelization I |
Slides | 2.1, 2.2, 2.6 | ||

May 16 |
L06: Kernelization II |
Slides | 2.3.1, 2.5, 2.4 | ||

May 23 |
L07: Kernelization III |
Slides | 9.1, 15.1 (intro) | Sheet 3 | May 30 |

May 30 |
L08: Kernelization Lower Bounds |
Slides | 15.1,15.2.2 | ||

June 6 |
L09: Algebraic Methods |
Slides | 10.1.1,10.1.2,10.4.1 | ||

June 13 |
No lecture |
||||

June 20 |
L10: Important Cuts |
Slides | 8.1, 8.2, 8.3, 8.5, 8.6 | Sheet 4 | June 27 |

June 20 |
L11: Treewidth I |
Slides | 7.1-7.4 | ||

July 4 |
L12: Treewidth II |
Slides | 11.2.1,14.5.2, 13.6.2 | ||

July 11 |
L13: Treewidth III |
Slides | 7.7 | Sheet 5 | July 18 |

July 18 |
L14: Turing and Lossy Kernelization |
Slides | 9.4, 23.1 and 23.4 from this book |

**Reference Textbook**

"Parameterized Algorithms" by Cygan et al. (see this for free pdf of the book from the authors).