Structural Parameterized Complexity
Jouke E. Witteveen
Abstract:
We revisit fixed-parameter tractability, fixed-parameter reducibility and kernelizability. The standard formulations of their definitions are enhanced for greater correctness from a structural complexity point of view. Doing so makes clear the distinction between fixed-parameter reducibility and kernelizability. Additionally, these time based definitions are augmented with space based counterparts. We then proceed to introduce an informativeness property for parameterized problems and define a measure for the computational complexity of individual instances of parameterized problems. By its construction, this measure embodies the idea that parameters capture complexity. This measure is lower bounded by the resource bounded Kolmogorov complexity, where the resource bound depends on the computational complexity of the parameterized problem.