New Horizons in Parameterized Complexity

Summary

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.