Recent developments in kernelization: A survey

Kernelization is a formalization of efficient preprocessing, aimed mainly at combinatorially hard problems. Empirically, preprocessing is highly successful in practice, e.g., in state-of-the-art SAT and ILP solvers. The notion of kernelization from parameterized complexity makes it possible to rigorously prove upper and lower bounds on, e.g., the maximum output size of a preprocessing in terms of one or more problem-specific parameters. This avoids the often-raised issue that we should not expect an efficient algorithm that provably shrinks every instance of any NP-hard problem. In this survey, we give a general introduction to the area of kernelization and then discuss some recent developments. After the introductory material we attempt a reasonably self-contained update and introduction on the following topics: (1) Lower bounds for kernelization, taking into account the recent progress on the and-conjecture. (2) The use of matroids and representative sets for kernelization. (3) Turing kernelization, i.e., understanding preprocessing that adaptively or non-adaptively creates a large number of