Kernelization, Partially Polynomial Kernels

Years and Authors of Summarized Original Work

• 2011; Betzler, Guo, Komusiewicz, Niedermeier

• 2013; Basavaraju, Francis, Ramanujan, Saurabh

• 2014; Betzler, Bredereck, Niedermeier

Problem Definition

In parameterized complexity, each instance (I, k) of a problem comes with an additional parameter k which describes structural properties of the instance, for example, the maximum degree of an input graph. A problem is called fixed-parameter tractable if it can be solved in f(k) ⋅ poly(n) time, that is, the super-polynomial part of the running time depends only on k. Consequently, instances of the problem can be solved efficiently if k is small.

One way to show fixed-parameter tractability of a problem is the design of a polynomial-time data reduction algorithm that reduces any input instance (I, k) to one whose size is bounded in k. This idea is captured by the notion of kernelization.

Definition 1

Let (I, k) be an instance of a parameterized problem P, where $I \in \varSigma ^{{\ast}}$...