Kernelization Techniques and Its Applications to Parameterized Computation

According to parameterized complexity theory,a decidable parameterized problem is fixed-parameter tractable if and only if it can be kernelized.Kernelization is the most widely applied and effective technique in the parameterized algorithm design.It is one of the hottest issues in parameterized complexity theory.This paper firstly introduces four main kernelization techniques,which are compared and analyzed with practical examples.Then it discusses how to apply these techniques to parameterized problems,such as covering problems,packing problems and cutting problems.Finally,the paper gives the future research directions about kernelization,especially the new possible kernelization technique and the kernel optimization of several FPT problems.