Parameterized Planar Dominating Set

Linear-Time Computation of a Linear Problem Kernel for Dominating Set on Planar Graphs

We present a linear-time kernelization algorithm that transforms a given planar graph G with domination number γ(G) into a planar graph G′ of size O(γ(G)) with γ(G) = γ(G′). In addition, a minimum dominating set for G can be inferred from a minimum dominating set for G′. In terms of parameterized algorithmics, this implies a linear-size problem kernel for the NP-hard Dominating Set problem on p...

Efficient Data Reduction for DOMINATING SET: A Linear Problem Kernel for the Planar Case

Dealing with the NP-complete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set on planar graphs has a so-called problem kernel of linear size, achieved by two simple and easy to implement reduction rules. This answers an open question from previous w...

Parameterized Planar Dominating Set 21

A note on parameterized exponential time complexity

In this paper we define the notion of an f(k)-uniform parameterized exponential time scheme. We show that a problem can be solved in parameterized O(2p(n)) time if and only if it has an f(k)-uniform parameterized exponential time scheme (p is a polynomial). We then illustrate how our formulation can be used to show that special instances of parameterized NPhard problems are as difficult as the ...

Improved kernel size for Planar Dominating Set

Determining whether a parameterized problem is kernelizable has recently become one of the most interesting topics of research in the area of parameterized complexity and algorithms. Theoretically, it has been proved that a parameterized problem is kernelizable if and only if it is fixed-parameter tractable. Practically, applying a data-reduction algorithm to reduce an instance of a parameteriz...