### 22.01.17 - 27.01.17, Seminar 17041

# Randomization in Parameterized Complexity

### Diese Seminarbeschreibung wurde vor dem Seminar auf unseren Webseiten veröffentlicht und bei der Einladung zum Seminar verwendet.

## Motivation

Randomization plays a prominent role in many subfields of theoretical computer science. Typically, this role is twofold: On the one hand, randomized methods can be used to solve essentially classical problems easier or more efficiently. In many cases, this allows for simpler, faster, and more appealing solutions for problems that have rather elaborate deterministic algorithms; in other cases, randomization provides the only known way to cope with the problem (e.g. polynomial identity testing, or deciding whether there exists a perfect matching with exactly *b* red edges in an edge-colored bipartite graph). On the other hand, there are also cases where randomness is intrinsic to the question being asked, such as the study of properties of random objects, and the search for algorithms which are efficient on average for various input distributions.

Parameterized complexity is an approach of handling computational intractability, where the main idea is to analyze the complexity of problems in finer detail by considering additional problem parameters beyond the input size. This area has enjoyed much success in recent years, and has yielded several new algorithmic approaches that help us tackle computationally challenging problems. While randomization already has an important role in parameterized complexity, for instance in techniques such as color-coding or randomized contractions, there is a common opinion within researchers of the field that the full potential of randomization has yet to be fully tapped.

In this seminar we hope to help bridge this gap, by bringing together experts in the areas of randomized algorithms and parameterized complexity. In doing so, we hope to:

- Establish domains for simpler and/or more efficient FPT algorithms via randomization.
- Identify problems which intrinsically need randomization.
- Study parameterized problems whose instances are generated by some underlying distribution.
- Stimulate the development of a broadened role of randomness within parameterized complexity.

**License**

Creative Commons BY 3.0 Unported license

Marek Cygan, Fedor V. Fomin, Danny Hermelin, and Magnus Wahlström