What's next? Future directions in parameterized complexity

Abstract

The progress in parameterized complexity has been very significant in recent years, with new research questions and directions, such as kernelization lower bounds, appearing and receiving considerable attention. This speculative article tries to identify new directions that might become similar hot topics in the future. First, we point out that the search for optimality in parameterized complexity already has good foundations, but lots of interesting work can be still done in this area. The systematic study of kernelization became a very successful research direction in recent years. We look at what general conclusions one can draw from these results and we argue that the systematic study of other algorithmic techniques should be modeled after the study of kernelization. In particular, we set up a framework for understanding which problems can be solved by branching algorithms. Finally, we discuss that the domain of directed graph problems is a challenging area which can potentially see significant progress in the following years. © 2012 Springer-Verlag Berlin Heidelberg.