January 20 – 25 , 2019, Dagstuhl Seminar 19041

New Horizons in Parameterized Complexity


Fedor V. Fomin (University of Bergen, NO)
Dániel Marx (Hungarian Academy of Sciences – Budapest, HU)
Saket Saurabh (Institute of Mathematical Sciences – Chennai, IN)
Meirav Zehavi (Ben Gurion University – Beer Sheva, IL)

For support, please contact

Dagstuhl Service Team


Dagstuhl Report, Volume 9, Issue 1 Dagstuhl Report
Aims & Scope
List of Participants
Dagstuhl's Impact: Documents available
Dagstuhl Seminar Schedule [pdf]


In 2019 the parameterized complexity (PC) community is celebrating two round dates: 30 years since the appearance of the paper of Abrahamson, Ellis, Fellows, and Mata in FOCS 1989, which can be considered as the starting point of PC, and 20 years since the appearance of the influential book of Downey and Fellows "Parameterized Complexity".

In these three decades, there has been tremendous progress in developing the area. The central vision of Parameterized Complexity through all these years has been to provide the algorithmic and complexity-theoretic toolkit for studying multivariate algorithmics in different disciplines and subfields of Computer Science. To achieve this vision, several algorithmic and complexity theoretic tools such as polynomial time preprocessing, aka kernelization, color-coding, graph-decompositions, parameterized integer programming, iterative compression, or lower bounds methods based on assumptions stronger than P=NP have been developed. These tools are universal as they did not only help in the development of the core of Parameterized Complexity, but also led to its success in other subfields of Computer Science such as Approximation Algorithms, Computational Social Choice, Computational Geometry, problems solvable in P (polynomial time) to name a few.

All cross-discipline developments result in flow of ideas and methods in both directions. In the last few years, we have witnessed several exciting developments of new parameterized techniques and tools in the following subfields of Computer Science and Optimization: Mathematical Programming, Computational Linear Algebra, Computational Counting, Derandomization, and Approximation Algorithms. A natural question is whether these domain-centric methods and tools are universal. That is, can they permeate boundaries of subfields and be employed wherever Parameterized Complexity approach can be used? The main objective of the seminar was to initiate the discussion on which of the recent domain-specific algorithms and complexity advances can become useful in other domains.

The seminar collected 46 participants from 18 countries. The participants presented their recent results in 26 invited and contributed talks. Open problems were discussed in open problem and discussion sessions.

Summary text license
  Creative Commons BY 3.0 Unported license
  Fedor V. Fomin, Dániel Marx, Saket Saurabh, and Meirav Zehavi

Related Dagstuhl Seminar


  • Data Structures / Algorithms / Complexity


  • Parameterized Complexity
  • Fixed-parameter tractability
  • Mathematical Programming
  • Approximation


In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.


Download overview leaflet (PDF).

Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.


Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.